5,276 results
Search Results
2. Role of adaptive intraspecific competition on collective behavior in the rock–paper–scissors game
- Author
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Junpyo Park and Bongsoo Jang
- Subjects
General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Statistical and Nonlinear Physics - Published
- 2023
3. Comment on the paper 'Second-grade fluid model with Caputo–Liouville generalized fractional derivative, Ndolane Sene, Chaos, Solitons and Fractals, 2020, 133, 109631'
- Author
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Asterios Pantokratoras
- Subjects
General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Statistical and Nonlinear Physics - Published
- 2022
4. Comment on the paper 'Solar energy aspects of gyrotactic mixed bioconvection flow of nanofluid past a vertical thin moving needle influenced by variable Prandtl number, Ying-Qing Song, Aamir Hamid, M. Ijaz Khan, R.J. Punith Gowda, R. Naveen Kumar, B.C. Prasannakumara, Sami Ullah Khan, M. Imran Khan, M.Y. Malik, Chaos, Solitons Fractals, 151, 2021, 111244'
- Author
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Asterios Pantokratoras
- Subjects
General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Statistical and Nonlinear Physics - Published
- 2022
5. Adaptive movement strategy in rock-paper-scissors models
- Author
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Tenorio, M., Rangel, E., and Menezes, J.
- Subjects
General Mathematics ,Applied Mathematics ,Populations and Evolution (q-bio.PE) ,FOS: Physical sciences ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Pattern Formation and Solitons (nlin.PS) ,Nonlinear Sciences - Pattern Formation and Solitons ,Nonlinear Sciences - Adaptation and Self-Organizing Systems ,Biological Physics (physics.bio-ph) ,Physics - Data Analysis, Statistics and Probability ,FOS: Biological sciences ,Physics - Biological Physics ,Quantitative Biology - Populations and Evolution ,Adaptation and Self-Organizing Systems (nlin.AO) ,Data Analysis, Statistics and Probability (physics.data-an) - Abstract
Organisms may respond to local stimuli that benefit or threaten their fitness. The adaptive movement behaviour may allow individuals to adjust their speed to maximise the chances of being in comfort zones, where death risk is minimal. We investigate spatial cyclic models where the rock-paper-scissors game rules describe the nonhierarchical dominance. We assume that organisms of one out of the species can control the mobility rate in response to the information obtained from scanning the environment. Running a series of stochastic simulations, we quantify the effects of the movement strategy on the spatial patterns and population dynamics. Our findings show that the ability to change mobility to adapt to environmental clues is not reflected in an advantage in cyclic spatial games. The adaptive movement provokes a delay in the spatial domains occupied by the species in the spiral waves, making the group more vulnerable to the advance of the dominant species and less efficient in taking territory from the dominated species. Our outcomes also show that the effects of adaptive movement behaviour accentuate whether most individuals have a long-range neighbourhood perception. Our results may be helpful for biologists and data scientists to comprehend the dynamics of ecosystems where adaptive processes are fundamental., Comment: 8 pages, 7 figures
- Published
- 2022
6. Comment on the paper 'One-parameter lie scaling study of carreau fluid flow with thermal radiation effects, Musharafa Saleem, Qasim Ali Chaudhry, A. Othman Almatroud, Chaos, Solitons and Fractals 148 (2021) 110996'
- Author
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Asterios Pantokratoras
- Subjects
General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Statistical and Nonlinear Physics - Published
- 2022
7. Evolutionary dynamics of rock-paper-scissors game in the patchy network with mutations
- Author
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Tina Verma and Arvind Kumar Gupta
- Subjects
Hopf bifurcation ,education.field_of_study ,General Mathematics ,Applied Mathematics ,Population ,Evolutionary game theory ,Biodiversity ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Metapopulation ,symbols.namesake ,Transcritical bifurcation ,Evolutionary biology ,Mutation (genetic algorithm) ,symbols ,education ,Evolutionary dynamics ,Mathematics - Abstract
Connectivity is the safety network for biodiversity conservation because connected habitats are more effective for saving the species and ecological functions. The nature of coupling for connectivity also plays an important role in the co-existence of species in cyclic-dominance. The rock-paper-scissors game is one of the paradigmatic mathematical model in evolutionary game theory to understand the mechanism of biodiversity in cyclic-dominance. In this paper, the metapopulation model for rock-paper-scissors with mutations is presented in which the total population is divided into patches and the patches form a network of complete graph. The migration among patches is allowed through simple random walk. The replicator-mutator equations are used with the migration term. When migration is allowed then the population of the patches will synchronized and attain stable state through Hopf bifurcation. Apart form this, two phases are observed when the strategies of one of the species mutate to other two species: co-existence of all the species phase and existence of one kind of species phase. The transition from one phase to another phase is taking place due to transcritical bifurcation. The dynamics of the population of species of rock, paper, scissors is studied in the environment of homogeneous and heterogeneous mutation. Numerical simulations have been performed when mutation is allowed in all the patches (homogeneous mutation) and some of the patches (heterogeneous mutation). It has been observed that when the number of patches is increased in the case of heterogeneous mutation then the population of any of the species will not extinct and all the species will co-exist.
- Published
- 2021
8. The interplay of rock-paper-scissors competition and environments mediates species coexistence and intriguing dynamics
- Author
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Mohd Hafiz Mohd and Junpyo Park
- Subjects
Abiotic component ,Dynamical systems theory ,Computer science ,General Mathematics ,Applied Mathematics ,media_common.quotation_subject ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Competition (biology) ,Bifurcation analysis ,Salient ,Homogeneous ,Attractor ,Quantitative Biology::Populations and Evolution ,Social ecological model ,Biological system ,media_common - Abstract
Asymmetrical rock-paper-scissors (RPS) competition has been perceived as a crucial factor in shaping species biodiversity, and understanding this ecological issue in a multi-species paradigm is rather difficult because community dynamics usually depend on distinct factors such as abiotic environments, biotic interactions and symmetry-breaking phenomenon. To address this problem, we employ a Lotka-Volterra competitive system consisting of both symmetrical, asymmetrical interactions and abiotic environment components. We discover that that asymmetrical RPS competition in heterogeneous environments can yield much richer dynamical behaviors, compared to the symmetrical and asymmetrical competition in homogeneous environments. While it is observed that species coexistence outcomes and/or oscillatory solutions are maintained as in the case of homogeneous environments, the nonuniformity in the environmental carrying capacities may lead to extra dynamics with regards to the appearance of survival states; for instance, coexistence of any two-species and single-species persistence states, which are not evident in the previous modelling studies. By means of bifurcation analysis, various salient features of the dynamical systems, including the emergence of certain attractors (e.g., different steady states, stable limit cycles and heteroclinic cycles) and co-dimension one bifurcations (e.g., transcritical and supercritical Hopf bifurcations) are realized in this ecological model. Overall, this modelling work provides a novel attempt to simultaneously encompass not only symmetry-breaking phenomenon through RPS competition, but also heterogeneity in the environments. This framework can provide additional insights to better understand various mechanisms underlying the effects of distinct ecological processes on multi-species communities.
- Published
- 2021
9. Evolutionary dynamics in the rock-paper-scissors system by changing community paradigm with population flow
- Author
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Junpyo Park
- Subjects
Hopf bifurcation ,education.field_of_study ,General Mathematics ,Applied Mathematics ,Population ,General Physics and Astronomy ,Robustness (evolution) ,Statistical and Nonlinear Physics ,Fixed point ,symbols.namesake ,symbols ,Outflow ,Statistical physics ,Balanced flow ,Evolutionary dynamics ,education ,Multistability ,Mathematics - Abstract
Classic frameworks of rock-paper-scissors game have been assumed in a closed community that a density of each group is only affected by internal factors such as competition interplay among groups and reproduction itself. In real systems in ecological and social sciences, however, the survival and a change of a density of a group can be also affected by various external factors. One of common features in real population systems in ecological and social sciences is population flow that is characterized by population inflow and outflow in a group or a society, which has been usually overlooked in previous works on models of rock-paper-scissors game. In this paper, we suggest the rock-paper-scissors system by implementing population flow and investigate its effect on biodiversity. For two scenarios of either balanced or imbalanced population flow, we found that the population flow can strongly affect group diversity by exhibiting rich phenomena. In particular, while the balanced flow can only lead the persistent coexistence of all groups which accompanies a phase transition through supercritical Hopf bifurcation on different carrying simplices, the imbalanced flow strongly facilitates rich dynamics such as alternative stable survival states by exhibiting various group survival states and multistability of sole group survivals by showing not fully covered but spirally entangled basins of initial densities due to local stabilities of associated fixed points. In addition, we found that, the system can exhibit oscillatory dynamics for coexistence by relativistic interplay of population flows which can capture the robustness of the coexistence state. Applying population flow in the rock-paper-scissors system can ultimately change a community paradigm from closed to open one, and our foundation can eventually reveal that population flow can be also a significant factor on a group density which is independent to fundamental interactions among groups.
- Published
- 2021
10. Call for papers: Special issue on evolutionary game theory of small groups and their larger societies
- Author
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Paolo Grigolini
- Subjects
Matching (statistics) ,Unification ,Management science ,General Mathematics ,Applied Mathematics ,Evolutionary game theory ,General Physics and Astronomy ,Behavioural sciences ,Statistical and Nonlinear Physics ,Complex network ,01 natural sciences ,Swarm intelligence ,010305 fluids & plasmas ,0103 physical sciences ,Synchronization (computer science) ,Sociology ,010306 general physics ,Team management - Abstract
This is a call for papers that should contribute to the unification of behavioral sciences and team management, focusing on the biological origin of cooperation and swarm intelligence, moving from biology to psychology and from sociology to political science, with the help of the theoretical tools of complex networks. This issue should shed light into the origin of ergodicity breaking and contribute to establishing a connection, still lacking theoretical support, between complexity properties that are expected to be correlated. Examples are: non-Poisson renewal events and multi-fractality; complexity matching and chaos synchronization; criticality and extended criticality of small size systems. Although the emphasis is on systems of small size, and especially on the search of the size maximizing both information transport and cooperation emergence, special attention will be devoted to the interaction between small groups and their larger societies.
- Published
- 2017
11. Notes to the paper 'Fixed points in intuitionistic fuzzy metric spaces' and its generalization to L-fuzzy metric spaces
- Author
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Reza Saadati
- Subjects
Discrete mathematics ,Mathematics::General Mathematics ,General Mathematics ,Applied Mathematics ,Injective metric space ,Fuzzy set ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,T-norm ,Cauchy sequence ,Convex metric space ,Metric space ,Fuzzy mathematics ,Metric map ,Mathematics - Abstract
Recently, Alaca et al. [Alaca et al., Chaos, Solitons & Fractals 2006;29:1073–9] proved some fixed point theorems in intuitionistic fuzzy metric spaces by a strong definition of Cauchy sequence (see [George and Veeramani, Fuzzy Sets Syst 1994;64:395–9] and [Veeramani and Vasuki, Fuzzy Sets Syst 2003;135:409–13]), also the intuitionistic fuzzy metric space has extra conditions (see [Gregori et al., Chaos, Solitons & Fractals, 2006;28:902–5]). In this paper, we consider generalized intuitionistic fuzzy metric spaces i.e., L -fuzzy metric spaces and prove the fuzzy version of Banach and Edelstein contraction theorems in these spaces for modified definition of Cauchy sequence.
- Published
- 2008
12. Complexity in Spacetime and Gravitation i. FromChaos to Superchaosfn2fn2This paper, as a token ofappreciation, is intended to celebrate the 57th birthday of Otto Rössler
- Author
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John Argyris, C. Ciubotariu, and Ioannis Andreadis
- Subjects
Physics ,Spacetime ,General Mathematics ,Applied Mathematics ,Spontaneous symmetry breaking ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Chaos theory ,Gravitation ,Theoretical physics ,Classical mechanics ,Theory of relativity ,Coordinate singularity ,Gravitational singularity ,Schwarzschild radius - Abstract
We intend to show in this paper that the two fundamental concepts of the GrandUnification and the Chaos Theory are essential constituent elements of a theory of everythingand appertain, in fact, to the overall domain of complexity in space, time and gravitation. Theauthors hope that the present paper may offer suggestions for the necessary methodology in theanalysis of complex problems. Following a short review of the main concepts describingconventional complexity, we introduce as an example of a possible development in standardparadigms, a new type of Rayleigh–Benard instability which maybe generated in the interior of a gravitating body and may be the cause of earthquakephenomena. We define the new terminologies of constructive and destructiveresonances in relation to the stability of the solar system. We attempt to find a physicalargument in support of the invariant character of a gravitational chaos. Within the frame of aRiemannian spacetime we obtain also a mathematical formulation of El Naschies conjecture: gravity is caused by an average deviation of fractal time from linear uniform time. Westudy also in some detail the physics of black holes because black holes offer perfect laboratoriesfor all manifestations of complexities and simplicities. We stress that singularities as well aschaos demonstrate an invariant character. Even the Schwarzschild radius, which was initiallyconsidered to be merely a coordinate singularity, is found to retain or deepen its physicalsignificance by diffeomorphisms. Symmetry principles in particle physics and continuousattempts to find a fundamental and unique constituent (strings, p-branes, etc.) of matter arereviewed and their link with complexity, dimensionality of spacetime and chaos is indicated.Particular attention is paid to spontaneous symmetry breaking and the Higgs mechanism in thecontext of a cascade of concepts: classical lattice gas, Ising model, order–disorder transition,inflationary scenario, and the universe as a lattice. This cascade tends to confirm the universalityof the lattice structure of the universe. In the final section of this first part of the paper wepropose a novel multi-spherical cosmic fractal as a model of homogeneous andisotropic cosmologies. If chaos is generated at the level of a background-arena in spacetime, thenadditional chaotic manifestations generated in this arena represent chaos on a higher level orscale. The suggestion is offered that a chaos on a higher level called superchaos interlaces withchaotic effects at different lower levels. The two other prospective parts of the paper will refer tothe subjects: Part 2. Chaoticity of Anisotropic Cosmologies. Part 3. Elementary Particles, DarkMatter and Information Aspects in Relativity.
- Published
- 1998
13. Von Neumann Geometry and E(∞) Quantum Spacetimefn1fn1This paper is dedicated to Itmor Procaccia, a personal friend and a fellow fighter for all those things which make life worth living like beauty, peace and justice, on the occasion of his birthday
- Author
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M.S. El Naschie
- Subjects
Physics::General Physics ,Mathematics::Operator Algebras ,General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Absolute geometry ,Geometry ,Quantum spacetime ,Quantum differential calculus ,General Relativity and Quantum Cosmology ,symbols.namesake ,Von Neumann algebra ,symbols ,Foundations of geometry ,Noncommutative quantum field theory ,Continuous geometry ,Synthetic geometry ,Mathematics ,Mathematical physics - Abstract
In this paper, it is shown that von Neumann continuous geometry may be regarded as the first attempt towards formulating a general quantum spacetime geometry akin to that of Cantorian spacetime E(∞) and noncommutative geometry.
- Published
- 1998
14. A new form of the early exercise premium for American type derivatives
- Author
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Tsvetelin S. Zaevski
- Subjects
General Mathematics ,Applied Mathematics ,Short paper ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Type (model theory) ,01 natural sciences ,Maturity (finance) ,Lévy process ,010305 fluids & plasmas ,Derivative (finance) ,0103 physical sciences ,Asset (economics) ,Put option ,010301 acoustics ,Mathematical economics ,Brownian motion ,Mathematics - Abstract
The purpose of this short paper is to present a new form of the so called early exercise premium for the American type derivatives. The decomposition we derived consists of the corresponding European derivative and a derivative with a stochastic maturity. In different particular cases we reach to the well known form for the American put option where the underlying asset is driven by a Brownian motion or a Levy process.
- Published
- 2019
15. A SUPPLEMENT TO THE PAPERS CONVERGENCE OF THE LAX–FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (II)—(III)
- Author
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Gui-Qiang Chen, Xiaxi Ding, and Peizhu Luo
- Subjects
Physics ,Isentropic process ,General Mathematics ,Scheme (mathematics) ,Convergence (routing) ,General Physics and Astronomy ,Applied mathematics ,Gas dynamics - Published
- 1989
16. The exceptional eightfold way to a possible Higgs field
- Author
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M.S. El Naschie
- Subjects
Physics ,Particle physics ,High energy ,Hierarchy ,General Mathematics ,Applied Mathematics ,Short paper ,Eightfold Way ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Symmetry group ,Invariant (physics) ,Theoretical physics ,Higgs field ,Brane cosmology - Abstract
The exceptional Lie symmetry groups are intimately connected to octions and build various forms of hierarchies. We show that these hierarchies have invariant total dimensions equal to a few well known key numbers of high energy elementary particle-like states. More specifically, the total dimension of E8, E7, E6, E5 and E4 is equal to N = 528 of Witten’s p = 5 Brane theory. Adding the standard model, then one can infer the possibility of a missing eight dimensional field akin to the Higgs field. The present short paper considers the various ramifications of the interplay between the exceptional Lie symmetry groups hierarchy and particle physics of the standard model.
- Published
- 2008
17. On two new fuzzy Kähler manifolds, Klein modular space and ’t Hooft holographic principles
- Author
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M.S. El Naschie
- Subjects
Connection (fibred manifold) ,Pure mathematics ,business.industry ,General Mathematics ,Applied Mathematics ,Short paper ,Holography ,General Physics and Astronomy ,Duality (optimization) ,Statistical and Nonlinear Physics ,Modular design ,Space (mathematics) ,Fuzzy logic ,law.invention ,High Energy Physics::Theory ,Theoretical physics ,law ,Mathematics::Differential Geometry ,business ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
This short paper outlines the basic topological features of two new fuzzy Kahler manifolds in duality. Relation to E-infinity theory of the compactified Klein modular space in connection with ’t Hooft holographic principles is briefly discussed.
- Published
- 2006
18. Asymptotic normality of parameters estimation in ev model with replicated observations
- Author
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Xiru Chen and Sanguo Zhang
- Subjects
Estimation ,General Mathematics ,General Physics and Astronomy ,Asymptotic distribution ,Applied mathematics ,Paper based ,Mathematics - Abstract
This paper based on the essay [1], studies in case that replicated observations are available in some experimental points, the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.
- Published
- 2002
19. Golden mean energy equals highest atomic electron orbital energy
- Author
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Leonard J. Malinowski
- Subjects
Physics ,Golden mean ,General Mathematics ,Applied Mathematics ,Short paper ,General Physics and Astronomy ,Electron orbital ,Statistical and Nonlinear Physics ,Golden ratio ,Electron configuration ,Atomic physics ,Energy (signal processing) - Abstract
The golden mean numerical value φ = 0.5(√5 − 1) has been given a physical manifestation through E infinity theory. This short paper relates the golden mean energy 0.618034 MeV to atomic electron orbitals.
- Published
- 2009
20. Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature. II. The general case
- Author
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Mikhail Smolyakov
- Subjects
Quantum Gases (cond-mat.quant-gas) ,General Mathematics ,Applied Mathematics ,FOS: Physical sciences ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Condensed Matter - Quantum Gases - Abstract
In the present paper, discussion of the canonical quantization of a weakly nonideal Bose gas at zero temperature within the framework of the Bogolyubov approach is continued. Contrary to the previous paper on this subject, here the two-body interaction potential is considered in the general form. It is shown that in such a case consideration of the first nonlinear correction also leads to the automatic particle number conservation without any additional assumptions or modification of the resulting effective Hamiltonian., 30 pages. Supplementary material: the standard Maxima .wxmx file is automatically unpacked by the arXiv upload software, so the .xml file, which can also be processed by Maxima, is uploaded instead. v2: major revision of the text, added references, minor corrections in ancillary files. v3: typos corrected
- Published
- 2023
21. Lie symmetry and invariants for a generalized Birkhoffian system on time scales
- Author
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Yi Zhang
- Subjects
General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Perturbation (astronomy) ,Statistical and Nonlinear Physics ,01 natural sciences ,Conserved quantity ,010305 fluids & plasmas ,0103 physical sciences ,Invariant (mathematics) ,Adiabatic process ,010301 acoustics ,Mathematical physics ,Mathematics - Abstract
The Lie symmetry and invariants for a generalized Birkhoffian system on time scales are studied, which include exact invariants and adiabatic invariants. First, the generalized Pfaff-Birkhoff principle on time scales is established, and by using Dubois-Reymond lemma the generalized Birkhoff’s equations on time scale are derived. Secondly, the determining equations of Lie symmetry for the generalized Birkhoffian system on time scales are established. We prove that if the Lie symmetry satisfies the structural equation, it leads to a conserved quantity, which is an exact invariant of the system. Again, the perturbation of Lie symmetry under the action of small disturbance is considered, the determining equations and the structural equations of disturbed system are established, and the adiabatic invariants led by the Lie symmetry perturbation for the generalized Birkhoffian system on time scales are given. Because of the arbitrariness of selecting time scales and the generality of the generalized Birkhoffian system, the results of this paper are of universal significance. The results of this paper contain the corresponding results for Birkhoffian system on time scales and classical generalized Birkhoffian system as its special cases. At the end of the paper, an example is given to illustrate the validity of the method and the results.
- Published
- 2019
22. Evolution of fractional-order chaotic economic systems based on non-degenerate equilibrium points
- Author
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Guoxing Zhang, Zhaoxian Su, and Pengxiao Qian
- Subjects
Equilibrium point ,Computer simulation ,General Mathematics ,Applied Mathematics ,Coordinate system ,Chaotic ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Bifurcation diagram ,Nonlinear system ,Economic system ,Entropy (arrow of time) ,Bifurcation ,Mathematics - Abstract
The economic system is an irreversible entropy increase process which is constructed by many elements and is far away from the equilibrium point; and affected by various parameters change, it is quite common that its motion state appears chaotic phenomenon due to instability. The extremely complex and not completely random aperiodic motion form of chaotic phenomenon is strongly sensitive to initial conditions. The development of nonlinear science, especially the emergence and development of chaos and fractal theory, has gradually become a powerful tool for economists to study the complexity, uncertainty and nonlinearity of social economic systems; and some visionary economists began to apply the research results of nonlinear science to economics, which has produced nonlinear economics. On the basis of summarizing and analyzing previous research works, this paper first obtains the non-degenerate equilibrium point of some typical fractional-order chaotic economic systems and transforms the equilibrium points of those systems to the origin through coordinate transformation, and then analyzes the Jacobi matrixes of new systems obtained through coordinate translation, and the parameter conditions of bifurcation in the economic systems are finally given and the numerical simulation of the fractional-order chaotic economic system evolution is carried out through bifurcation diagram, phase diagram and time series diagram. The study results of this paper provide a reference for the further study of the evolution of fractional-order chaotic economic systems with non-degenerate equilibrium points.
- Published
- 2019
23. Research on application of fractional calculus in signal real-time analysis and processing in stock financial market
- Author
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Hui Wang
- Subjects
Stochastic volatility ,Computer science ,General Mathematics ,Applied Mathematics ,Financial market ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,01 natural sciences ,Stock market index ,010305 fluids & plasmas ,Variance-gamma distribution ,Fractional calculus ,0103 physical sciences ,Econometrics ,Financial modeling ,Stock market ,Time series ,010301 acoustics - Abstract
In this paper, the author proposes a new stock financial market stochastic volatility and stock pricing model based on the Taylor formula, by embedding the strictly increasing harmonic steady-state process as a time variable into the Brownian motion with drift terms. The use of variance gamma and normal inverse high-lower distribution are special forms of NTS distribution, combined with principal component analysis (PCA) and artificial neural network (ANN) methods, for nonlinear and multi-scale complex financial time series in financial markets. The model is constructed and predicted, and the forecast and calculation of stock market index and foreign exchange rate are realized. Through calculation and research, the model can fill the blank of complex time series model research in financial market. The stock signal analysis based on fractional calculus equation proposed in the thesis is based on the idea of decomposition-reconstruction-integration, which can improve the prediction accuracy of the model for the time series combined financial model. The Shanghai and Shenzhen 300 Index and foreign exchange rates selected by the paper are taken from the market real data, and the skeleton prediction model is established. It can predict the short-term trend after the stock market closes, confirming the nonlinear, multi-scale and non-stationary the prediction accuracy of the sequential decomposition prediction method of financial time series is effectively improved, and the principal component and artificial neural network method are used to compress redundant data and shorten the prediction time.
- Published
- 2019
24. Existence and multiplicity for some boundary value problems involving Caputo and Atangana–Baleanu fractional derivatives: A variational approach
- Author
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Amjad Salari and Behzad Ghanbari
- Subjects
General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Multiplicity (mathematics) ,01 natural sciences ,Boundary values ,010305 fluids & plasmas ,Fractional calculus ,Nonlinear system ,Variational method ,0103 physical sciences ,Applied mathematics ,Boundary value problem ,Fractional differential ,010301 acoustics ,Mathematics - Abstract
In this paper, we study the existence and the numerical estimates of solutions for a specific types of fractional differential equations. The nonlinear part of the problem, however, presupposes certain hypotheses. Particularly, for exact localization of the parameter, the existence of a non-zero solution is established, which requires the sublinearity of the nonlinear part at the origin and infinity. We also take into consideration several theoretical and numerical examples. One of the main novelties of this paper is to use the variational method to investigate the properties of solutions of boundary values problems involving Atangana–Baleanu fractional derivative for the first time.
- Published
- 2019
25. Differential and integral operators with constant fractional order and variable fractional dimension
- Author
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Abdon Atangana and Anum Shafiq
- Subjects
Computer science ,General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Order (ring theory) ,Statistical and Nonlinear Physics ,01 natural sciences ,Fractal dimension ,Integral equation ,010305 fluids & plasmas ,Dimension (vector space) ,0103 physical sciences ,Doors ,Applied mathematics ,Differential (infinitesimal) ,Constant (mathematics) ,010301 acoustics ,Variable (mathematics) - Abstract
The complexities of nature have pushed humankind to construct complex mathematical formula that can be used to capture such natural occurrence. Very recently the concept differential and integral operators with fractional order and fractal dimension were introduced. The concept has opened new doors for investigations. In this paper, we present a step forward, where the constant fractal dimension is replaced by variable dimension. We present in detail some properties of this new operators, we suggested a new numerical approach that can be used to solve differential and integral equations associate to this operators. We presented some examples and simulations are presented to underpin the strength of the new operators. We strongly believe that this paper will open many new doors of investigation toward modeling real world problems.
- Published
- 2019
26. Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator
- Author
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Zhong, Ming and Yan, Zhenya
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,General Mathematics ,Applied Mathematics ,Classical Physics (physics.class-ph) ,FOS: Physical sciences ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Physics - Classical Physics ,Pattern Formation and Solitons (nlin.PS) ,Nonlinear Sciences - Pattern Formation and Solitons ,Machine Learning (cs.LG) ,Exactly Solvable and Integrable Systems (nlin.SI) - Abstract
In this paper, we firstly extend the Fourier neural operator (FNO) to discovery the soliton mapping between two function spaces, where one is the fractional-order index space $\{\epsilon|\epsilon\in (0, 1)\}$ in the fractional integrable nonlinear wave equations while another denotes the solitonic solution function space. To be specific, the fractional nonlinear Schr\"{o}dinger (fNLS), fractional Korteweg-de Vries (fKdV), fractional modified Korteweg-de Vries (fmKdV) and fractional sine-Gordon (fsineG) equations proposed recently are studied in this paper. We present the train and evaluate progress by recording the train and test loss. To illustrate the accuracies, the data-driven solitons are also compared to the exact solutions. Moreover, we consider the influences of several critical factors (e.g., activation functions containing Relu$(x)$, Sigmoid$(x)$, Swish$(x)$ and $x\tanh(x)$, depths of fully connected layer) on the performance of the FNO algorithm. We also use a new activation function, namely, $x\tanh(x)$, which is not used in the field of deep learning. The results obtained in this paper may be useful to further understand the neural networks in the fractional integrable nonlinear wave systems and the mappings between two spaces., Comment: 17 pages, 20 figures
- Published
- 2022
27. Probabilistic responses of three-dimensional stochastic vibro-impact systems
- Author
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Wei Xu, Shichao Ma, Xiaole Yue, Xin Ning, and Liang Wang
- Subjects
Computer science ,General Mathematics ,Applied Mathematics ,Response analysis ,Monte Carlo method ,Probabilistic logic ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Context (language use) ,Probability density function ,01 natural sciences ,010305 fluids & plasmas ,Transformation (function) ,0103 physical sciences ,Applied mathematics ,Relief valve ,Reduction (mathematics) ,010301 acoustics - Abstract
Chatter between devices becomes a primary concern in actual engineering problems since it may cause the reduction of efficiency. Due to random factors and non-smooth properties, difficulties rest in deriving the analytical results and such systems are generally investigated with simplified approximate methods. In this context, the present paper pioneers the response analysis of three-dimensional hydraulic relief valve impact systems under stochastic excitations. In order to retain the non-smooth characteristics of the systems under consideration, no non-smooth transformation is imposed on the original system. A procedure in which the stochastic trajectories start from the contact surface and return to the contact surface for the next time is constructed. Probability density functions (PDFs) of the random trajectories returning to the contact surface at any time can be obtained, and the proposed procedure is proved accurate and efficient using Monte Carlo (MC) simulations in this paper. Moreover, we find that the flow rate of the systems can lead to the stochastic P-bifurcation on the contact surface. Further discussion indicates that the proposed procedure can substantially reflect the complicated dynamic behaviors of the high-dimensional vibro-impact systems.
- Published
- 2019
28. New results on regional observer-based stabilization for locally Lipchitz nonlinear systems
- Author
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Muhammad Shahid Nazir, Syeda Rabiya Hamid, Muhammad Rehan, and Haroon ur Rashid
- Subjects
Observer (quantum physics) ,Computer science ,General Mathematics ,Applied Mathematics ,Chaotic ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Decoupling (cosmology) ,Lipschitz continuity ,01 natural sciences ,010305 fluids & plasmas ,Range (mathematics) ,Nonlinear system ,Robustness (computer science) ,Control theory ,0103 physical sciences ,010301 acoustics - Abstract
This paper describes the design of a regional observer-based controller for the locally Lipchitz nonlinear systems, which can be employed successfully to attain both monitoring and control of a wide range of systems. An observer-based control approach has been employed to attain advantages of the traditional state feedback along with the state estimation through an observer. A lot of work has been accomplished for the globally Lipchitz nonlinear systems. However, a less conservative continuity, called the generalized ellipsoidal Lipchitz condition, has been applied in this paper to consider the locally Lipchitz systems. This condition is then incorporated to attain convex routines for computing the local controller and observer gains. The focus of the present study is to investigate conditions for simultaneous design of observer and controller under locally Lipchitz nonlinearities for systems with norm-bounded disturbances that not only guarantees the stabilization and true state estimation but also robustness against external perturbations. Furthermore, the decoupling of the observer and controller design conditions has been worked out for obtainment of a simple design method. Since the resultant control approach applies to a general class of systems, it can be straightforwardly employed to the globally Lipschitz nonlinear systems as a specific case. The approach is tested via a chaotic system and simulation results are provided to validate the effectiveness of resultant control schemes for the locally Lipschitz systems.
- Published
- 2019
29. Behavioural study of symbiosis dynamics via the Caputo and Atangana–Baleanu fractional derivatives
- Author
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Kolade M. Owolabi
- Subjects
Dynamical systems theory ,General Mathematics ,Applied Mathematics ,Dynamics (mechanics) ,Chaotic ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Pattern generation ,01 natural sciences ,Fractional power ,010305 fluids & plasmas ,Fractional calculus ,Linear stability analysis ,0103 physical sciences ,Time derivative ,Applied mathematics ,010301 acoustics ,Mathematics - Abstract
Research findings have shown that evolution equations containing non-integer order derivatives can lead to some useful dynamical systems which can be used to describe important physical scenarios. This paper deals with numerical simulations of multicomponent symbiosis systems, such as the parasitic predator-prey model, the commensalism system, and the mutualism case. In such models, we replace the classical time derivative with either the Caputo fractional derivative or the Atangana-Baleanu fractional derivative in the sense of Caputo. To guide in the correct choice of parameters, we report the models linear stability analysis. Numerical examples and results obtained for different instances of fractional power α are provided for non-spatial models as well as the spatial case in one and two dimensions in other to justify our theoretical findings which include the chaotic phenomena, spatiotemporal and oscillatory patterns, multiple steady states and other spatial pattern processes. This paper further suggest an alternative approach to incessant killing of wildlife animals for pattern generation and decorative purposes.
- Published
- 2019
30. Theme and sentiment analysis model of public opinion dissemination based on generative adversarial network
- Author
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Hu Yingxi, Haihong E, Zhao Wen, Xiao Siqi, Niu Peiqing, and Peng Hai-Peng
- Subjects
Computer science ,business.industry ,General Mathematics ,Applied Mathematics ,Information sharing ,Deep learning ,Sentiment analysis ,Control variable ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Public opinion ,Machine learning ,computer.software_genre ,01 natural sciences ,010305 fluids & plasmas ,0103 physical sciences ,Benchmark (computing) ,Leverage (statistics) ,Social media ,Artificial intelligence ,business ,010301 acoustics ,computer - Abstract
An epidemic is a typical public health emergency that refers to the occurrence and rapid spread of disease. A good epidemic transmission model plays a crucial role in preventing an epidemic. The epidemic transmission model is largely similar to the model of sentiment analysis and transmission on social media. Therefore, this paper intend to use the method of deep learning to explore the key issues of theme and sentiment analysis from the perspective of public opinion analysis. In order to fully extract the features automatically, we combine the following methods: multi-channel inputs, multi-granularity convolution kernels, direct connection with high-speed channels, and this paper proposes the multi-channel and multi-kernel (MCMK) model. Furthermore, we leverage generative adversarial nets to combine several single tasks, called Joint-MCMK model, which achieves information sharing and improves the training speed and model accuracy. To verify the validity of our proposed models, this paper experimented with the short text topic classification dataset TREC [1] and the sentiment analysis dataset IMDB [2] . Results achieved 98.6% and 92.6% respectively, which are superior to the highest existing industry benchmark (96.1% and 92.58%). In addition, this paper compared the training spread differences between the joint-MCMK model and MCMK model, which shows that the joint-MCMK model has better performance at training speed. Finally, the control variable method was used to analyze the multiple effects of the different factors. The optimal value of some relevant parameters in our models were verified by several experiments.
- Published
- 2019
31. System of fractional differential algebraic equations with applications
- Author
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Babak Shiri and Dumitru Baleanu
- Subjects
Constant coefficients ,General Mathematics ,Applied Mathematics ,Numerical analysis ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,01 natural sciences ,010305 fluids & plasmas ,Fractional calculus ,Algebraic equation ,Singularity ,0103 physical sciences ,Applied mathematics ,Algebraic number ,010301 acoustics ,Differential algebraic equation ,Differential (mathematics) - Abstract
One of the important classes of coupled systems of algebraic, differential and fractional differential equations (CSADFDEs) is fractional differential algebraic equations (FDAEs). The main difference of such systems with other class of CSADFDEs is that their singularity remains constant in an interval. However, complete classifying and analyzing of these systems relay mainly to the concept of the index which we introduce in this paper. For a system of linear differential algebraic equations (DAEs) with constant coefficients, we observe that the solvability depends on the regularity of the corresponding pencils. However, we show that in general, similar properties of DAEs do not hold for FDAEs. In this paper, we introduce some practical applications of systems of FDAEs in physics such as a simple pendulum in a Newtonian fluid and electrical circuit containing a new practical element namely fractors. We obtain the index of introduced systems and discuss the solvability of these systems. We numerically solve the FDAEs of a pendulum in a fluid with three different fractional derivatives (Liouville–Caputo’s definition, Caputo–Fabrizio’s definition and with a definition with Mittag–Leffler kernel) and compare the effect of different fractional derivatives in this modeling. Finally, we solved some existing examples in research and showed the effectiveness and efficiency of the proposed numerical method.
- Published
- 2019
32. Fractal description of the complex beatings: How to describe quantitatively seismic waves?
- Author
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P.N. Alexandrov, Raoul R. Nigmatullin, K. S. Nepeina, and Artem S. Vorobev
- Subjects
Property (programming) ,Computer science ,General Mathematics ,Applied Mathematics ,Structure (category theory) ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,01 natural sciences ,Signal ,Seismic wave ,010305 fluids & plasmas ,Fractal ,Component (UML) ,Compression (functional analysis) ,0103 physical sciences ,010301 acoustics ,Algorithm ,Scaling - Abstract
In this paper, we suggest a new algorithm for description of complex beatings. Under the complex beating we understand a signal, which contains the high-frequency (HF) component that is located between two low-frequency (LF) envelopes having random origin. These beatings are associated with the so-called blow-like signals (BLS) and a typical example of the BLS can be associated with the registered earthquakes signals. For description of these signals, it becomes possible to separate two envelopes from the HF-component located between them and find their amplitude-frequency response (AFR) based on the non-orthogonal amplitude-frequency analysis of the smoothed signals (NAFASS) approach that was suggested earlier by one of the authors (RRN) in paper [1] . It was successfully applied for description of economic data having also multi-frequency structure. In order to separate these envelopes from the HF component one can notice that the most signals of such kind have a fractal (self-similar) structure. It means that under reasonable compression/scaling of these signals they keep approximately their initial structure. This scaling property can be tested on many types of the different signals. In the results of application of the NAFASS approach one can describe quantitatively the desired envelopes and obtain their AFRs. As an example, we considered the randomly taken data that were recorded from EQs station located in Kyrgyzstan. We deliberately chose the different types of the EQs signals in order to demonstrate the flexibility and wide applicability of the proposed algorithm. We expect that this algorithm can find a wide application for description of many BLS that are met frequently in many natural phenomena and engineering applications.
- Published
- 2019
33. Using rewards reasonably: The effects of stratified-rewards in public goods game
- Author
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Qiao Chen, Tong Chen, and Ran Yang
- Subjects
Self-assessment ,Scope (project management) ,General Mathematics ,Applied Mathematics ,Control (management) ,General Physics and Astronomy ,Face (sociological concept) ,Statistical and Nonlinear Physics ,01 natural sciences ,Standard deviation ,010305 fluids & plasmas ,Asynchronous communication ,0103 physical sciences ,Public goods game ,Business ,Marketing ,010301 acoustics - Abstract
This paper is inspired by the stratified-rewards adopted by rural organizers. Since this method has been used for many years, this paper attempts to explore the feasibility of it. We take into account of individuals’ self-assessment of face, asynchronous decision-making and individuals’ expectations for their neighbors, take available funds and standard deviation as the main indicators and then use agent-based model to simulate the effects of stratified-rewards. Our results show that cooperation can be maintained or promoted slightly if the total number of individuals who can gain rewards is not large. If organizers want to gain more available funds, they need to expand the scope of reward. But they should control the number of individuals who can receive higher rewards this time. Otherwise, the available funds may less than the initial value, though all individuals choose to cooperate. Of course, controlling costs is also important. In general, organizers can get more available funds at low cost if they do it properly.
- Published
- 2019
34. Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system
- Author
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You Li, Xiaojie Hou, Shihong Zhong, and Jin-Liang Wang
- Subjects
Period-doubling bifurcation ,General Mathematics ,Applied Mathematics ,Chaotic ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Lyapunov exponent ,Instability ,symbols.namesake ,Bifurcation theory ,Discrete time and continuous time ,symbols ,Statistical physics ,Bifurcation ,Center manifold ,Mathematics - Abstract
This paper is concerned with the spatiotemporal behaviors of a Gierer–Meinhardt system in discrete time and space form. Through the linear stability analysis, the parametric conditions are gained to ensure the stability of the homogeneous steady state of the system. Based on the bifurcation theory, as well as center manifold theorem, we derive the critical parameter values of the flip, Neimark–Sacker and Turing bifurcation respectively. Besides, the specific parameter expression to form patterns are also determined. In order to identify chaos among regular behaviors, we calculate the Maximum Lyapunov exponents. The results obtained in this paper are illustrated by numerical simulations. From the simulations, we can see some complex dynamics, such as period doubling cascade, invariant cycles, periodic windows, chaotic behaviors, and some striking Turing patterns, e.g. circle, mosaic, spiral, spatiotemporal chaotic patterns and so on, which can be produced by flip-Turing instability, Neimark–Sacker–Turing instability and chaos.
- Published
- 2019
35. Edge extraction of mineralogical phase based on fractal theory
- Author
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Li Shanshan, Jin Donghao, Lin Honglei, and Yang Aimin
- Subjects
Random field ,Pixel ,Noise (signal processing) ,General Mathematics ,Applied Mathematics ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,General Physics and Astronomy ,020206 networking & telecommunications ,Statistical and Nonlinear Physics ,02 engineering and technology ,Fractal dimension ,Peak signal-to-noise ratio ,Fractal ,Dimension (vector space) ,Computer Science::Computer Vision and Pattern Recognition ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Algorithm ,Histogram equalization ,Mathematics - Abstract
In order to understand the microstructure of pellets and improve the metallurgical properties of pellets, fractal theory is introduced to extract the edge features of pellets. Firstly, the original mineralogical phase is obtained by experiment, which is preprocessed by the histogram equalization to enhance the overall contrast. Based on the discrete Fractional Brownian Random Field Model, the algorithm is redesigned to calculate the dimension of each pixel, map the gray space of image into the dimension space, select the appropriate window size, transform and edge extraction. Comparing the algorithm in this paper with Canny operator and Laplace–Gauss operator, it is concluded that the algorithm in this paper has certain advantages in mineralogical phase edge extraction. Then, Gauss noise is added to the original gray image, and Canny operator and this algorithm are used to extract the edges of the noisy image. The numerical results of peak signal to noise ratio and root mean square error are obtained. Finally, the comparison proves that the algorithm can extract more complete edges, and has a stronger noise immunity.
- Published
- 2018
36. Modeling the dynamics of Hepatitis E with optimal control
- Author
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Ebraheem O. Alzahrani and Muhammad Altaf Khan
- Subjects
General Mathematics ,Applied Mathematics ,Dynamics (mechanics) ,Control variable ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Derivative ,Optimal control ,Hepatitis E ,medicine.disease ,01 natural sciences ,Stability (probability) ,010305 fluids & plasmas ,Stability theory ,0103 physical sciences ,medicine ,Applied mathematics ,010306 general physics ,Control (linguistics) ,Mathematics - Abstract
The present paper shows the dynamics of Hepatitis E with optimal control. The paper is analyzed by two different aspects: first, we explore the dynamics of Hepatitis E model and then applying the optimal control analysis. Secondly, we use the most appropriate and recent fractional order derivative called the Atangana–Baleanu derivative for the dynamical analysis of Hepatitis E model. The proposed model considered is locally asymptotically stable when the threshold quantity less than one. Further, we explore the stability analysis of the model when R 0 > 1 . Then, we choose some appropriate control to formulate the optimality system. The results associated to the optimal control are obtained and discussed with different strategies. Moreover, we apply Atangana–Baleanu derivative to the proposed model and obtain the required results necessary for the fractional order model. Numerical results for the optimal control problem and Atangana–Baleanu derivative are obtained and discussed in detail. The results suggest that control variables chosen should be properly applied to get rid of the infection of Hepatitis E. The Atangana–Baleanu derivative results suggest that at any time t we can check the disease status and make a useful strategy for the early elimination of Hepatitis E from the community.
- Published
- 2018
37. Conservation of a predator species in SIS prey-predator system using optimal taxation policy
- Author
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Nishant Juneja and Kulbhushan Agnihotri
- Subjects
Hopf bifurcation ,Equilibrium point ,Biomass (ecology) ,education.field_of_study ,General Mathematics ,Applied Mathematics ,Population ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,01 natural sciences ,010305 fluids & plasmas ,Predation ,010101 applied mathematics ,symbols.namesake ,0103 physical sciences ,symbols ,Econometrics ,Prey predator ,0101 mathematics ,education ,Predator ,Bifurcation ,Mathematics - Abstract
In this paper, we present and analyze a prey-predator system, in which prey species can be infected with some disease. The model presented in this paper is motivated from D. Mukherjee’s model in which he has considered an SI model for the prey species. There are substantial evidences that infected individuals have the ability to recover from the disease if vaccinated/ treated properly. In this regard, Mukherjee’s model is modified by considering SIS model for prey species. Theoretical and numerical simulations show that the recovery of infected prey species plays a crucial role in eliminating the limit cycle oscillations and thus making the interior equilibrium point stable. The possibility of Hopf bifurcation around non zero equilibrium point using the recovery rate as a bifurcation parameter, is discussed. Further, the model is extended by incorporating the harvesting of predator population. A monitory agency has been introduced which monitors the exploitation of resources by implementing certain taxes for each unit biomass of the predator population. The main purpose of the present research is to explore the effect of recovery rate of prey on the dynamics of the system and to optimize the total economical net profits from harvesting of predator species, taking taxation as control parameter.
- Published
- 2018
38. Weak dissipation drives and enhances Wada basins in three-dimensional chaotic scattering
- Author
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Diego S. Fernández, Jesús M. Seoane, and Miguel A.F. Sanjuán
- Subjects
General Mathematics ,Applied Mathematics ,FOS: Physical sciences ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Chaotic Dynamics (nlin.CD) ,Nonlinear Sciences - Chaotic Dynamics - Abstract
Chaotic scattering in three dimensions has not received as much attention as in two dimensions so far. In this paper, we deal with a three-dimensional open Hamiltonian system whose Wada basin boundaries become non Wada when the critical energy value is surpassed in the absence of dissipation. In particular, we study here the dissipation effects on this topological change, which has no analogy in two dimensions. Hence, we find that non-Wada basins, expected in the absence of dissipation, transform themselves into partially Wada basins when a weak dissipation reduces the system energy below the critical energy. We provide numerical evidence of the emergence of the Wada points on the basin boundaries under weak dissipation. According to the paper findings, Wada basins are typically driven, enhanced and, consequently, structurally stable under weak dissipation in three-dimensional open Hamiltonian systems., Comment: 18 pages, 9 figures
- Published
- 2022
39. Envelope solitons of the nonlinear discrete vertical dust grain oscillation in dusty plasma crystals
- Author
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Alphonse Houwe, Souleymanou Abbagari, Mustafa Inc, Gambo Betchewe, Serge Y. Doka, Kofane T. Crépin, and Mühendislik ve Doğa Bilimleri Fakültesi
- Subjects
Dusty Plasma Crystals ,Physics ,Dusty plasma ,Nonlinear system ,Oscillation ,General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Envelope Solitons ,Atomic physics ,Discrete Vertical Dust Grain ,Envelope (waves) - Abstract
The paper concerns envelope soliton propagating through the nonlinear transverse dust grain displacement in dusty plasma crystals. The work found its motivation from the recent paper of the authors [7]. To reach the goal of this study we establish the linear dispersion and the nonlinear Schrödinger equation (NLSE) by employing the quasi discrete approximation [7,13–15]. Contrary to ref. [7], it is observed one additional regime of the formation of the dark soliton while choosing the gap frequency value (ωg≈150sec−) which is close to the experimental value given by Motcheyo et al. [7], Tsopgue et al. To corroborate the prediction made analytically to group velocity, was confirmed by numerical and experimental studies. As, it is established that in general manner the modulated waves describing by the NLSE can be stable or unstable to the perturbation, the modulation instability of steady state have been done. Despite, that the bandwidth of the model has been reduced compared to [7,13–15], we can say without hesitation that this work will be a capital contribution in dusty plasma crystal.
- Published
- 2022
40. Gas path parameter prediction of aero-engine based on an autoregressive discrete convolution sum process neural network
- Author
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Shisheng Zhong, Minghang Zhao, Zhiqi Yan, and Zhiquan Cui
- Subjects
Weight function ,Artificial neural network ,Computer science ,General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Network topology ,Backpropagation ,Convolution ,Autoregressive model ,Discrete time and continuous time ,Time series ,Algorithm - Abstract
In order to improve the approximation ability of neural network to functional and improve the prediction accuracy of time series data, this paper proposes an autoregressive discrete convolution sum process neural network prediction model and applies it to the prediction of aero-engine gas path performance parameters. Coupling threshold wavelet de-noising method is applied to the preprocessing of engine gas path parameters, which can effectively remove the noise in the time series data. Process neurons are applied to artificial neural networks to expand the computational functions of artificial neurons. The process neuron can not only realize the spatial aggregation operation of discrete input data and the connection weight, but also realize the time aggregation operation of the product integral of the continuous input function and the connection weight function. The output of discrete time series is affected by the current input/output, and also by the historical input/output value. Therefore, an autoregressive feedback link is added to the network topology, and the value of the network's output node is used as the input to adjust the network connection weight. The convolution sum operation of discrete time series data can realize the time accumulation effect, so the discrete convolution sum operator is used to replace the integral operator to realize the time aggregation function of the process neuron. Since the integral operation of the continuous function is avoided, the weight training process of the process neural network is effectively simplified, and the accuracy loss in the continuous-time function fitting process of discrete input samples is effectively avoided. Bayesian regularization network weight learning algorithm is used to solve the problems of slow convergence speed and easy to fall into local optimum of back propagation learning algorithm, and improve the generalization ability of neural network. It can be seen from the prediction simulation results of the two engines that the average relative error and root mean square error of the engine gas path parameter prediction based on the autoregressive discrete convolution sum process neural network model can be reduced to 0.67% and 0.35 respectively. The stable and high-precision prediction results show that the network model and weight learning algorithm proposed in this paper have better robustness in functional approximation, and have higher accuracy in time series data prediction.
- Published
- 2022
41. On periodic solutions of a second-order, time-delayed, discontinuous dynamical system
- Author
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Albert C. J. Luo and Liping Li
- Subjects
Dynamical systems theory ,General Mathematics ,Applied Mathematics ,010102 general mathematics ,Constraint (computer-aided design) ,Mathematical analysis ,General Physics and Astronomy ,Order (ring theory) ,Boundary (topology) ,Motion (geometry) ,Statistical and Nonlinear Physics ,Phase plane ,Dynamical system ,01 natural sciences ,010101 applied mathematics ,Flow (mathematics) ,0101 mathematics ,Mathematics - Abstract
This paper develops the analytical conditions for the existence of periodic solutions of a second-order,time-delayed, discontinuous dynamical system. A sample model consists of two linear delayed sub-systems with a switching boundary. The defined G-functions for the delayed, discontinuous systems are introduced, and sufficient and necessary conditions for a flow crossing, sliding and grazing along the switch boundary are developed for such a delayed, discontinuous system. Furthermore, nine (9) regular basic mappings in phase plane and thirty-three (33) delay-related mappings for the second-order, time-delayed, discontinuous systems are classified. Constraint equations are predicted analytically for two periodic orbits with initial functions provided posteriorly. Finally, three numerical examples are illustrated to verify the existence of generalized slowly oscillating periodic orbits without and with sliding portions. This paper improves and extends motion switchability conditions at the boundary in discontinuous dynamical systems without delay.
- Published
- 2018
42. Analytic solutions for variance swaps with double-mean-reverting volatility
- Author
-
Jeong Hoon Kim and See Woo Kim
- Subjects
Variance swap ,050208 finance ,Stochastic volatility ,General Mathematics ,Applied Mathematics ,05 social sciences ,Monte Carlo method ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,01 natural sciences ,Heston model ,010104 statistics & probability ,Nonlinear system ,0502 economics and business ,Mean reversion ,Applied mathematics ,0101 mathematics ,Volatility (finance) ,Closed-form expression ,Mathematics - Abstract
A three factor variance model introduced by Gatheral in 2008, called the double mean reverting (DMR) model, is well-known to reflect the empirical dynamics of the variance and prices of options on both SPX and VIX consistently with the market. One drawback of the DMR model is that calibration may not be easy as no closed form solution for European options exists, not like the Heston model. In this paper, we still use the double mean reverting nature to extend the Heston model and study the pricing of variance swaps given by simple returns in discrete sampling times. The constant mean level of Heston’s stochastic volatility is extended to a slowly varying process which is specified in two different ways in terms of the Ornstein-Uhlenbeck (OU) and Cox-Ingersoll-Ross (CIR) processes. So, two types of double mean reversion are considered and the corresponding models are called the double mean reverting Heston-OU model and the double mean reverting Heston-CIR models. We solve Riccati type nonlinear equations and derive closed form exact solutions or closed form approximations of the fair strike prices of the variance swaps depending on the correlation structure of the three factors. We verify the accuracy of our analytic solutions by comparing with values computed by Monte Carlo simulation. The impact of the double mean reverting formulation on the fair strike prices of the variance swaps are also scrutinized in the paper.
- Published
- 2018
43. Fractality and singularity in CME linear speed signal: Cycle 23
- Author
-
Anup Kumar Bhattacharjee, Anirban Chattopadhyay, and Mofazzal H. Khondekar
- Subjects
Physics ,Hurst exponent ,General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Solar cycle 23 ,Statistical and Nonlinear Physics ,Multifractal system ,01 natural sciences ,010305 fluids & plasmas ,Singularity ,Physics::Space Physics ,0103 physical sciences ,Detrended fluctuation analysis ,Astrophysics::Solar and Stellar Astrophysics ,Statistical physics ,Time series ,Singularity spectrum ,010303 astronomy & astrophysics ,Scaling - Abstract
In the recent past, coronal mass ejection (CME) has received much research attention for its geo-effectiveness. In this paper, an investigation has been made to identify the scaling pattern of the CME linear speed time series data (February 1999 to December 2007 of solar cycle 23) collected from the Solar and Heliospheric Observatory (SOHO) using Multi-Fractal Detrended Fluctuation Analysis (MFDFA) and Multi-Fractal Detrended Moving Average (MFDMA) method. The scaling exponent, generalized Hurst exponent, singularity strength and also the singularity spectrum have been computed to quantify the multifractality and to identify the singularities of the time series data. An effort has also been made to find out the possible sources which are responsible for the multifractality in the signal by studying the scaling patterns of the shuffled and surrogate version of the original data. It has been revealed in this paper that CME linear speed signal exhibit multifractal behaviour with long-term persistence. Both the long-range temporal correlation and the broad probability density function (pdf) are found to be the primary source of multifractality in the signal. The singularities or abruptness present in the signal are found to vary with time, and this fluctuation follows an AR (2) model.
- Published
- 2018
44. The agglomeration phenomenon influence on the scaling law of the scientific collaboration system
- Author
-
Ai-Zhong Shen, Jin-Li Guo, Guo-Lin Wu, and Shu-Wei Jia
- Subjects
Hypergraph ,Theoretical computer science ,Property (programming) ,Computer science ,Economies of agglomeration ,General Mathematics ,Applied Mathematics ,Node (networking) ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,Phenomenon ,0103 physical sciences ,symbols ,Pareto distribution ,010306 general physics ,Cluster analysis ,Clustering coefficient - Abstract
This paper presents a scientific collaboration hypernetwork evolution model with adjustable clustering coefficient in which the authors are regarded as nodes and the hyperedges are the cooperative articles. Firstly, we build the scientific cooperation hypernetwork through the real paper data which comes from the database of arxive. The empirical results show that the node's hyperdegree follows the power law distribution, but the hyperedge's node-degree has the exponent distribution. In addition, we establish the scientific collaboration clustering hypernetwork evolution model by employing the Poisson process theory and the continuous method for studying the agglomeration phenomenon of scientific cooperation system. The theoretical analysis shows that the node's hyperdegree distribution has scale-free characteristics. The power index of our model is independent of the clustering coefficient, and the theoretical analyses agree with the conducted numerical simulations. Moreover, our model not only describes the scale-free property, but also depicts the phenomenon of agglomeration. Both the properties are usually coexist in the scientific cooperation, our model is more actual.
- Published
- 2018
45. Fractional derivatives with no-index law property: Application to chaos and statistics
- Author
-
Abdon Atangana and José Francisco Gómez-Aguilar
- Subjects
Dynamical systems theory ,Differential equation ,General Mathematics ,Applied Mathematics ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Function (mathematics) ,Differential operator ,01 natural sciences ,Square (algebra) ,010305 fluids & plasmas ,Fractional calculus ,Law ,0103 physical sciences ,Attractor ,010306 general physics ,Analytic function ,Mathematics - Abstract
Recently fractional differential operators with non-index law properties have being recognized to have brought new weapons to accurately model real world problems particularly those with non-Markovian processes. This present paper has two double aims, the first was to prove the inadequacy and failure of index law fractional calculus and secondly to show the application of fractional differential operators with no index law properties to statistic and dynamical systems. To achieve this, we presented the historical construction of the concept of fractional differential operators from Leibniz to date. Using a matrix based on the fractional differential operators, we proved that, fractional operators obeying index law cannot model real world problems taking place in two states, more precisely they cannot describe phenomena taking place beyond their boundaries, as they are scaling invariant, more precisely our results show that, mathematical models based on these differential operators are not able to describe the inverse memory, meaning the full history of a physical problem cannot be described accurately using these derivatives with index law properties. On the other hand, we proved that, differential operators with no index-law properties are scaling variant, thus can describe situations taking place in different states and are able to localize the frontiers between two states. We present the renewal process properties included in differential equation build out of the Atangana–Baleanu fractional derivative and counting process, which is connected to its inter-arrival time distribution Mittag–Leffler distribution which is the kernel of these derivatives. We presented the connection of each derivative to a statistical family, for instance Riemann–Liouville–Caputo derivatives are connected to the Pareto statistic, which has no well-defined average when alpha is less than 1 corresponding to the interval where fractional operators mostly defined. We established new properties and theorem for the Atangana–Baleanu derivative of an analytic function, in particular we proved that, they are convolution of the Mittag–Leffler function with the Riemann–Liouville–Caputo derivatives. To see the accuracy of the non-index law derivative to in modeling real chaotic problems, 4 examples were considered, including the nine-term 3-D novel chaotic system, King Cobra chaotic system, the Ikeda delay system and chaotic chameleon system. The numerical simulations show very interesting and novel attractors. The king cobra system with the Atangana–Baleanu presented a very novel attractor where at the earlier time we observed a random walk and latter time we observed the real sharp of the cobra. The Ikeda model with Atangana–Baleanu presented different attractors for each value of fractional order, in particular we obtain a square and circular explosions. The results obtained in this paper show that, the future of modeling real world problem relies on fractional differential operators with non-index law property. Our numerical results showed that, to not model physical problems with fractional differential operators with non-singular kernel and imposing index law in fractional calculus is rightfully living with closed eyes without ever taking a risk to open them.
- Published
- 2018
46. Localization of disordered harmonic chain with long-range correlation
- Author
-
Hiroaki Yamada
- Subjects
Physics ,Condensed matter physics ,Phonon ,General Mathematics ,Applied Mathematics ,Wave packet ,FOS: Physical sciences ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Lyapunov exponent ,Condensed Matter - Disordered Systems and Neural Networks ,01 natural sciences ,010305 fluids & plasmas ,Exponential function ,Bernoulli's principle ,symbols.namesake ,Distribution (mathematics) ,Amplitude ,0103 physical sciences ,Harmonic ,symbols ,010306 general physics - Abstract
In the previous paper [Yamada, Chaos, Solitons $\&$ Fractals, {\bf 109},99(2018)], we investigated localization properties of one-dimensional disordered electronic system with long-range correlation generated by modified Bernoulli (MB) map. In the present paper, we report localization properties of phonon in disordered harmonic chains generated by the MB map. Here we show that Lyapunov exponent becomes positive definite for almost all frequencies $\omega$ except $\omega=0$, and the $B-$dependence changes to exponential decrease for $B > 2 $, where $B$ is a correlation parameter of the MB map. The distribution of the Lyapunov exponent of the phonon amplitude has a slow convergence, different from that of uncorrelated disordered systems obeying a normal central-limit theorem. Moreover, we calculate the phonon dynamics in the MB chains. We show that the time-dependence of spread in the phonon amplitude and energy wave packet changes from that in the disordered chain to that in the periodic one, as the correlation parameter $B$ increases., Comment: 10 pages, 11 figures
- Published
- 2018
47. Finite-time anti-synchronization of memristive stochastic BAM neural networks with probabilistic time-varying delays
- Author
-
Wenbing Zhao, Weiping Wang, Linlin Liu, Manman Yuan, and Xiong Luo
- Subjects
Lyapunov function ,0209 industrial biotechnology ,Artificial neural network ,Computer science ,General Mathematics ,Applied Mathematics ,Nonlinear control law ,Probabilistic logic ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,02 engineering and technology ,Memristor ,Synchronization ,law.invention ,symbols.namesake ,020901 industrial engineering & automation ,law ,Control theory ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,020201 artificial intelligence & image processing ,Bidirectional associative memory ,Finite time - Abstract
This paper investigates the drive-response finite-time anti-synchronization for memristive bidirectional associative memory neural networks (MBAMNNs). Firstly, a class of MBAMNNs with mixed probabilistic time-varying delays and stochastic perturbations is first formulated and analyzed in this paper. Secondly, an nonlinear control law is constructed and utilized to guarantee drive-response finite-time anti-synchronization of the neural networks. Thirdly, by employing some inequality technique and constructing an appropriate Lyapunov function, some anti-synchronization criteria are derived. Finally, a number simulation is provided to demonstrate the effectiveness of the proposed mechanism.
- Published
- 2018
48. A new chaotic model for glucose-insulin regulatory system
- Author
-
Payam Sadeghi Shabestari, Julien Clinton Sprott, Shirin Panahi, Sajad Jafari, and Boshra Hatef
- Subjects
Computer science ,General Mathematics ,Applied Mathematics ,Insulin ,medicine.medical_treatment ,Chaotic ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Computational biology ,Hypoglycemia ,medicine.disease ,01 natural sciences ,010305 fluids & plasmas ,0103 physical sciences ,Attractor ,medicine ,Feature (machine learning) ,Hyperinsulinemia ,Set (psychology) ,010301 acoustics - Abstract
For non-invasively investigating the interaction between insulin and glucose, mathematical modeling is very helpful. In this paper, we propose a new model for insulin-glucose regulatory system based on the well-known prey and predator models. The results of previous researches demonstrate that chaos is a common feature in complex biological systems. Our results are in accordance with previous studies and indicate that glucose-insulin regulatory system has various dynamics in different conditions. One interesting feature of this new model is having hidden attractor for some set of parameters. The result of this paper might be helpful for better understanding of regulatory system that contains glucose, insulin, and diseases such as diabetes, hypoglycemia, and hyperinsulinemia.
- Published
- 2018
49. Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm
- Author
-
Samir A. M. Martins, Márcio J. Lacerda, Márcia L. C. Peixoto, and Erivelton G. Nepomuceno
- Subjects
Logarithm ,Dynamical systems theory ,General Mathematics ,Applied Mathematics ,Computation ,Rounding ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Lyapunov exponent ,Interval (mathematics) ,01 natural sciences ,Upper and lower bounds ,010305 fluids & plasmas ,symbols.namesake ,0103 physical sciences ,Line (geometry) ,symbols ,Applied mathematics ,010301 acoustics ,Mathematics - Abstract
It has been shown that natural interval extensions (NIE) can be used to calculate the largest positive Lyapunov exponent (LLE). However, the elaboration of NIE are not always possible for some dynamical systems, such as those modelled by simple equations or by Simulink-type blocks. In this paper, we use rounding mode of floating-point numbers to compute the LLE. We have exhibited how to produce two pseudo-orbits by means of different rounding modes; these pseudo-orbits are used to calculate the Lower Bound Error (LBE). The LLE is the slope of the line gotten from the logarithm of the LBE, which is estimated by means of a recursive least square algorithm (RLS). The main contribution of this paper is to develop a procedure to compute the LLE based on the LBE without using the NIE. Additionally, with the aid of RLS the number of required points has been decreased. Eight numerical examples are given to show the effectiveness of the proposed technique.
- Published
- 2018
50. Dark solitons behaviors for a (2+1)-dimensional coupled nonlinear Schrödinger system in an optical fiber
- Author
-
Zhong-Zhou Lan, Bo Gao, and Ming-Jing Du
- Subjects
Physics ,Asymptotic analysis ,Optical fiber ,Field (physics) ,General Mathematics ,Applied Mathematics ,One-dimensional space ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Astrophysics::Cosmology and Extragalactic Astrophysics ,Bilinear form ,01 natural sciences ,010305 fluids & plasmas ,law.invention ,Nonlinear system ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Amplitude ,law ,Quantum mechanics ,0103 physical sciences ,Soliton ,010306 general physics ,Nonlinear Sciences::Pattern Formation and Solitons - Abstract
In this paper, we investigate a (2+1)-dimensional coupled nonlinear Schrodinger system, which describes the transverse effects in an optical fiber, time-independent copropagation and field of optical soliton. Bilinear forms, dark one- and two-soliton solutions are derived by virtue of the Hirota method. Propagation and interaction properties of the dark solitons are discussed: (i) Amplitudes and velocities of the dark solitons are affected by the values of the wave numbers μ, λ and θ. (ii) Head-on and overtaking interactions between the two parallel dark solitons are discussed, where the amplitudes of the dark solitons remain unchanged after each interaction, implying that the interactions are elastic. (iii) Stationary dark solitons are depicted in this paper. (iv) Through the asymptotic analysis, elastic interaction between the two solitons is discussed analytically.
- Published
- 2018
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