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In order to describe the self-similarity and long-range dependence of financial asset prices, this paper adopts a new fractional-type process, i.e, the generalized mixed weighted fractional Brownian motion to describe the dynamic change process of risky asset prices. A European option pricing model driven by the generalized mixed weighted fractional Brownian motion is constructed, and explicit solutions to the pricing formulas of European call options and European put options are derived by using the arbitrage-free pricing theory. Finally, through numerical simulation, the influence of the parameter on the option price is analyzed. [ABSTRACT FROM AUTHOR]

The primary varicella-zoster virus (VZV) infection that causes chickenpox (also known as varicella), spreads quickly among people and, in severe circumstances, can cause to fever and encephalitis. In this paper, the Mittag-Leffler fractional operator is used to examine the mathematical representation of the VZV. Five fractional-order differential equations are created in terms of the disease's dynamical analysis such as S: Susceptible, V: Vaccinated, E: Exposed, I: Infectious and R: Recovered. We derive the existence criterion, positive solution, Hyers–Ulam stability, and boundedness of results in order to examine the suggested fractional-order model's wellposedness. Finally, some numerical examples for the VZV model of various fractional orders are shown with the aid of the generalized Adams–Bashforth–Moulton approach to show the viability of the obtained results. [ABSTRACT FROM AUTHOR]

The social life, economic issues, and health issues resulting from various diseases will be impacted by the use of the epidemiological model to address the negative effects of drinking in society. The paper aims to investigate a nonlinear drinking epidemic fractional SHTR model in the sense of a Constant Proportional Caputo (CPC) operator. For the CPC operator, a stability study of the fractional order model and the presence of a solution have been made. A nonlinear system of the suggested system has an approximative solution provided by the Laplace Adomian Decomposition technique. A convergence analysis of the system is also treated to show the effect and efficiency of the scheme. Additionally, we offer some numerical outcomes to demonstrate the efficiency of this operator. A comparative study for different values of α shows that these methods are effective for giving better results in fractional order as compared to classical order derivatives. [ABSTRACT FROM AUTHOR]

This paper proposes a new four-dimensional hyper-chaotic system capable of generating multi-wing chaotic attractors by introducing active magnetron memristors, multi-segmented square functions and trigonometric functions. The dynamical properties of this new hyper-chaotic system, such as equilibrium point, dissipation, Lyapunov exponential spectrum, bifurcation diagram and Poincaré cross-section and attraction basin, are analyzed theoretically and simulated numerically, and the complexity of this system with different parameters is analyzed. It is observed that this hyper-chaotic system has periodic, chaotic and hyper-chaotic variations with an infinite number of equilibria and coexisting attractors under different parameter conditions. The circuit simulation was performed using Multisim and the results obtained were consistent with the numerical analysis of the dynamics, and the chaotic circuit system is designed by FPGA to verify the realizability of the system. Finally, an image encryption algorithm is designed in conjunction with the DNA algorithm to enable a new system chaotic sequence for image encryption. The results show that the hyper-chaotic system has rich dynamical behavior and has high-security performance when applied to image encryption with strong chaotic key and plaintext sensitivity and large key space in image encryption. [ABSTRACT FROM AUTHOR]

The regulation of energy associated with heat transfer is the most important problem in the food processing, chemical and biomedical engineering industries. Therefore, this investigation explores the heat transfer qualities of micropolar hybrid-nanofluid also considering entropy generation which has recently become central focus of research in the field of heat transfer processes. The purpose of this analysis is to explore the influence of magnetohydrodynamics (MHD), viscous dissipation, and heat radiation on the flow of hybrid-nanofluid with micropolar properties above an exponentially shrinking/stretching sheet. A mathematical model is constructed and the solution is acquired by utilizing numerical technique bvp-4c in MATLAB. The befitting usage of the second law of thermal physics helped in conducting the entropy production analysis. The study obtains numerical results for the governing equations, which reveal dual solutions when analyzing a shrinking sheet, contrary to a stretching sheet. The paper presents graphical depictions of the influence of different attributes upon micro-rotation, velocity, surface-friction, temperature, Nusselt number and also the entropy generation plus the Bejan number. Moreover, a comparison of heat transfer rates between conventional nanomaterial and hybrid-nanofluid is provided. The study concludes that dual solutions appear and the wall shear stress coefficient decreases as the values of micropolar parameter R 1 increase with critical values of λ being λ c = − 1. 2 8 , − 1. 3 4 and − 1. 3 7. Also thermal irreversibility, which results from fluid friction near the sheet rather than far from it, is more dominant than total entropy generation. [ABSTRACT FROM AUTHOR]

In this research paper, the authors wish to examine the effects of couple stress on hybrid nanofluid considering magnetohydrodynamic three-dimensional transient flow between two parallel plates. Stretching of the lower plate causes fluid flow in the channel. The fluid flow model is shown in mathematical form using a set of coupled nonlinear partial differential equations, which are then translated into coupled nonlinear ordinary differential equations using the proper transformation. The authors used the spectral quasi linearization method (SQLM), an effective numerical technique, to solve the updated equations and study the effects of various flow parameters on fluid temperature and velocity. The Nusselt number and skin friction coefficients were also investigated from an engineering standpoint. The generated solutions are verified using the residual analysis. Statistical analysis is performed on the skin-friction coefficients and the Nusselt number using quadratic regression models. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical behavior of the modified May–Holling–Tanner model in the presence of dynamic alternative resources. We study the role of dynamic alternative resources on the survival of the species when there is prey rarity. Detailed mathematical analysis and numerical evaluations, including the situation of ecosystem collapsing, have been presented to discuss the coexistence of species', stability, occurrence of different bifurcations (saddle-node, transcritical, and Hopf) in three cases in the presence of prey and alternative resources, in the absence of prey and in the absence of alternative resources. It has been obtained that the multiple coexisting states and their stability are outcomes of variations in predation rate for alternative resources. Also, the occurrence of Hopf bifurcation, saddle-node bifurcation, and transcritical bifurcation are due to variations in the parameters of dynamic alternative resources. The impact of dynamic alternative resources on species' density reveals the fact that if the predation rate for alternative resources increases, then the prey biomass increases (under some restrictions), and variations in the predator's biomass widely depend upon the quality of food items. This study also points out that the survival of predators is possible in the absence of prey. In the theme of ecological balance, this study suggests some theoretical points of view for the eco-managers. [ABSTRACT FROM AUTHOR]

This paper conducts a numerical analysis of the behavior of the average value of the Maximum Local Time, L n ∗ , in the Simple Random Walk on the square lattice. It has been established in the literature that the sequence ζ n : = (log n) 2 L n ∗ converges to π. The author found numerical evidence that the average value of ζ n ( ζ n ¯) increases until a certain value of n , denoted as n c , after which it decreases and approaches π. Furthermore, estimates are presented for n c and ζ n c ¯. [ABSTRACT FROM AUTHOR]

In this paper, we reproduce the rotation curve of the Andromeda galaxy (M31) by taking into account its bulge, disk and halo components, considering the last one to contain the major part of dark matter mass. Hence, our prescription is to split the galactic bulge into two components, namely, the inner and main bulges, respectively. Both bulges are thus modeled by exponential density profiles since we underline that the widely accepted de Vaucouleurs law fails to reproduce the whole galactic bulge rotation curve. In addition, we adopt various well-known phenomenological dark matter profiles to estimate the dark matter mass in the halo region. Moreover, we apply the least-squares fitting method to determine from the rotation curve the model free parameters, namely, the characteristic (central) density, scale radius and consequently the total mass. To do so, we perform Markov chain Monte Carlo statistical analyses based on the Metropolis algorithm, maximizing our likelihoods adopting velocity and radii data points of the rotation curves. We do not fit separately the components for bulges, disk and halo, but we perform an overall fit including all the components and employing all the data points. Thus, we critically analyze our corresponding findings and, in particular, we employ the Bayesian information criterion to assess the most accredited model to describe M31 dark matter dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability, accuracy and convergence behavior of various numerical schemes for phase-field modeling through a simple ODE model. Both theoretical analysis and numerical experiments are carried out on this ODE model to demonstrate the limitation of most numerical schemes that have been used in practice. One main conclusion is that the first-order fully implicit scheme is the only robust algorithm for phase-field simulations while all other schemes (that have been analyzed) may have convergence issue if the time step size is not exceedingly small. More specifically, by rigorous analysis in most cases, we have the following conclusions: (i) The first-order fully implicit scheme converges to the correct steady state solution for all time step sizes. In the case of multiple solutions, one of the solution branches always converges to the correct steady state solution. (ii) The first-order convex splitting scheme, which is equivalent to the first-order fully implicit scheme with a different time scaling, always converges to the correct steady state solution but may seriously lack numerical accuracy for transient solutions. (iii) For the second-order fully implicit and convex splitting schemes, for any time step size δ t > 0 , there exists an initial condition u 0 , with | u 0 | > 1 , such that the numerical solution converges to the wrong steady state solution. (iv) For | u 0 | ≤ 1 , all second-order schemes studied in this paper converge to the correct steady state solution although severe numerical oscillations occur for most of them if the time step size is not sufficiently small. (v) An unconditionally energy-stable scheme (such as the modified Crank–Nicolson scheme) is not necessarily better than a conditionally energy-stable scheme (such as the Crank–Nicolson scheme). Most, if not all, of the above conclusions are expected to be true for more general Allen–Cahn and other phase-field models. [ABSTRACT FROM AUTHOR]

In this paper, we investigate properties of the conserved charge in general relativity, recently proposed by one of the present authors with his collaborators, in the inflation era, the matter dominated era and the radiation dominated era of the expanding Universe. We show that the conserved charge in the inflation era becomes the Bekenstein–Hawking entropy for de Sitter space, and it becomes the matter entropy and the radiation entropy in the matter and radiation dominated eras, respectively, while the charge itself is always conserved. These properties are qualitatively confirmed by a numerical analysis of a model with a scalar field and radiations. Results in this paper provide more evidences on the interpretation that the conserved charge in general relativity corresponds to entropy. [ABSTRACT FROM AUTHOR]

This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin–Berezovskaya predator–prey model in depth using analytical and numerical bifurcation analysis. The stability conditions of fixed points, codim-1 and codim-2 bifurcations to include multiple and generic bifurcations are studied. This model exhibits transcritical, flip, Neimark–Sacker, and 1 : 2 , 1 : 3 , 1 : 4 strong resonances. The normal form coefficients and their scenarios for each bifurcation are examined by using the normal form theorem and bifurcation theory. For each bifurcation, various types of critical states are calculated, such as potential transformations between the one-parameter bifurcation point and different bifurcation points obtained from the two-parameter bifurcation point. To validate our analytical findings, the bifurcation curves of fixed points are determined by using MatcontM. [ABSTRACT FROM AUTHOR]

In this paper, stability-prone circular shallow arches composed of three symmetrically arranged flexibly bonded layers with fixed and hinged supports at both ends are examined. Based on the differential equations of equilibrium and a series expansion of the governing kinematic variables, analytical expressions for the limit points and bifurcation points are derived. Solutions for the nonlinear equilibrium path are also provided. Comparison with the results of much more complex numerical analyses with 2D finite continuum elements show high accuracy of these analytical expressions. The application examples indicate the importance of considering the flexibility of the interlayers in the stability analysis. With the assumption of a rigid bond between the layers, the stability limit is overestimated by up to 100% in the examples considered. [ABSTRACT FROM AUTHOR]

A recent quantum-geometrical approach for the possible reconciliation of the principles of general relativity and quantum mechanics extends the fundamental tensor to the relativistic (quantum) scales, in which additional geometric structures and curvatures, i.e., additional sources of gravitation, are emerged. This paper introduces some characteristics of the emerged curvatures and their consequences on regulating the space and initial singularities. We analyze the timelike geodesic congruence in the simplest solutions of the Einstein field equations; the homogeneous, isotropic, and spherically symmetric Schwarzschild, de Sitter–Schwarzschild, and Friedmann–Lemaitre–Robertson–Walker (FLRW) metrics. From the expansion of the trajectory congruence that follows the change in the shape of the volume which keeps the same set of geodesics in the bundle along the flow lines which are generated by the velocity fields, we conclude that the analytical and numerical analyses give an unambiguous signature that the space and initial singularities are attenuated or even regulated, especially in the relativistic (quantum) regime. This means that the regulation of the singularity in Einstein's general relativity (GR) would not be possible until quantum-mechanical ingredients are properly imposed on it. [ABSTRACT FROM AUTHOR]

This paper developed the dynamics of opinion network where a node interacts with only one node in each step and these nodes will not exchange their opinions until the difference of their opinions is below a tolerance threshold. Every node is a Gaussian fuzzy set with the center representing an opinion itself and a standard deviation characterizing an uncertainty about the opinion. The fuzzy opinion network with different uncertainties' levels of nodes was investigated to show how opinions and their uncertainties propagate and evolve for reaching a consensus in the network. The theoretical and numerical analyses were used to assess the conditions where a consensus can be reached in the fuzzy opinion network. [ABSTRACT FROM AUTHOR]

Hepatic injury induced by blunt abdominal impact is a major cause of death in vehicle crashes. However, few works have been done effectively in cadaver experiments to clarify the liver's specific dynamic behavior and mechanical characteristics. This paper described the dynamic behavior and mechanical characteristics of the liver under blunt impacts to the upper abdomen with the finite element model (FEM) of the Chinese human body — the 50 percentile-sized male (CHUBM-M50). The simulation matrix, three directions (frontal, oblique, lateral), and four speeds included in each group were designed with a 23.4 kg, rigid cylindrical impactor aligning the T11 level. The liver deformation contours displayed compression against the spine and rotation in the horizontal plane, which were the two main features in liver motion. Pressure distribution in the liver capsule and parenchyma was discussed to elucidate the biomechanical characteristics related to impact direction. Generally, the stress distribution in the capsule was 10 times higher than that in the parenchyma. A discussion of the injury mechanism of the liver capsule and parenchyma observed in the simulations was given upon the pressure distribution. It demonstrated that the capsule could protect liver parenchyma at low-speed impacts and should not be neglected for understanding liver injury mechanisms. [ABSTRACT FROM AUTHOR]

Nowadays, more and more federated learning algorithms have been implemented in edge computing, to provide various customized services for mobile users, which has strongly supported the rapid development of edge intelligence. However, most of them are designed relying on the reliable device-to-device communications, which is not a realistic assumption in the wireless environment. This paper considers a realistic aggregation problem for federated learning in a single-hop wireless network, in which the parameters of machine learning models are aggregated from the learning agents to a parameter server via a wireless channel with physical interference constraint. Assuming that all the learning agents and the parameter server are within a distance Γ from each other, we show that it is possible to construct a spanning tree to connect all the learning agents to the parameter server for federated learning within O (log Γ) time steps. After the spanning tree is constructed, it only takes O (log Γ) time steps to aggregate all the training parameters from the learning agents to the parameter server. Thus, the server can update its machine learning model once according to the aggregated results. Theoretical analyses and numerical simulations are conducted to show the performance of our algorithm. [ABSTRACT FROM AUTHOR]

Track irregularity is the main factor that affects the safety and comfort of high-speed railway. It is important to study the influence of the track irregularity on the safety service of high speed train–track coupling system. In this paper, a vehicle–track spatial nonlinear coupled system dynamics model is developed with FEM. The model includes vehicle subsystem and track subsystem, which are coupled by wheel–rail interface. The vehicle subsystem is a 31-DOF spatial vehicle model, and the track subsystem is a three-dimensional slab track model composed of the rail, rail pad and track slab. Considering wheel tread profile and rail head profile, the wheel–rail spatial contact geometry relationship is established, and the "Trace method" and the "Minimum distance method" are used to search for wheel–rail contact points. Considering the nonlinear contact between the wheel and the rail, a numerical approach is presented, where the "Trace method" is embedded into the algorithm for solving the vehicle–track nonlinear coupling dynamics equation by cross iteration, realizing searching the wheel–rail contact points and solving the vehicle–track nonlinear coupling equation simultaneously, which greatly improves the efficiency of numerical analysis. As application examples, the dynamic responses of a high speed train–track spatial nonlinear coupled system excited by the track V-shaped local profile irregularity and the track torsional irregularity are analyzed. The results show that the algorithm is effective in solving the vehicle–track spatial nonlinear coupled system dynamics problem, and the track irregularity has significant influence on the dynamic response of vehicle and track structure. [ABSTRACT FROM AUTHOR]

Compared with the clearance-sealed pistonphone, the membrane-sealed pistonphone can realize the sound pressure at very low frequency and very high sound pressure for its lower leakage. However, the membrane-sealed pistonphone also brings the problem that the compressed volume cannot be decided precisely because of the deformation of the membrane, which results in the inaccurate calculation for the sound pressure in the chamber. In this paper, a sound pressure formula for the membrane-sealed pistonphone is derived according to an analysis of the characteristics of the ideal membrane. The static and the dynamic deformation of the membrane are studied. Then, the effects of the thickness, the sealed width, the extension ratio, and the modal vibration of the membrane are studied through the finite element method. The results show that the deviation of the sound pressure level obtained from the ideal sound pressure formula can be reduced to less than 0.1 dB when the sound pressure level is lower than 174 dB and the membrane is specially designed, which indicates that the influence of the membrane on the sound pressure is almost negligible. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of numerical solution and stability of a chemostat model under fractal-fractional order derivative. First, we investigate the positivity and roundedness of the solution of the considered system. Second, we find the existence of a solution of the considered system by employing the Banach and Schauder fixed-point theorems. Furthermore, we obtain a sufficient condition that allows the existence of the stabling of solutions by using the numerical-functional analysis. We find that the proposed system exists as a unique positive solution that obeys the criteria of Ulam–Hyers (U-H) and generalized U-H stability. We also establish a numerical analysis for the proposed system by using a numerical scheme based on the Lagrange interpolation procedure. Finally, we provide two numerical examples to verify the correctness of the theoretical results. We remark that the structure described by the considered model is also sometimes called side capacity or cross-flow model. The structure considered here can be also seen as a limiting case of the pattern chemostats in parallel with diffusion connection. Moreover, the said model forms in natural and engineered systems and can significantly affect the hydrodynamics in porous media. Fractal calculus is an excellent tool to discuss fractal characteristics of porous media and the characteristic method of the porous media. [ABSTRACT FROM AUTHOR]

This paper investigates the mathematical properties of a stochastic version of the balanced 2D thermal quasigeostrophic (TQG) model of potential vorticity dynamics. This stochastic TQG model is intended as a basis for parametrization of the dynamical creation of unresolved degrees of freedom in computational simulations of upper ocean dynamics when horizontal buoyancy gradients and bathymetry affect the dynamics, particularly at the submesoscale (250 m–10 km). Specifically, we have chosen the Stochastic Advection by Lie Transport (SALT) algorithm introduced in [D. D. Holm, Variational principles for stochastic fluid dynamics, Proc. Roy. Soc. A: Math. Phys. Eng. Sci.471 (2015) 20140963, http://dx.doi.org/10.1098/rspa.2014.0963 ] and applied in [C. Cotter, D. Crisan, D. Holm, W. Pan and I. Shevchenko, Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model, Found. Data Sci.2 (2020) 173, https://doi.org/10.3934/fods.2020010 ; Numerically modeling stochastic lie transport in fluid dynamics, SIAM Multiscale Model. Simul.17 (2019) 192–232, https://doi.org/10.1137/18M1167929 ] as our modeling approach. The SALT approach preserves the Kelvin circulation theorem and an infinite family of integral conservation laws for TQG. The goal of the SALT algorithm is to quantify the uncertainty in the process of up-scaling, or coarse-graining of either observed or synthetic data at fine scales, for use in computational simulations at coarser scales. The present work provides a rigorous mathematical analysis of the solution properties of the thermal quasigeostrophic (TQG) equations with SALT [D. D. Holm and E. Luesink, Stochastic wave-current interaction in thermal shallow water dynamics, J. Nonlinear Sci.31 (2021), https://doi.org/10.1007/s00332-021-09682-9 ; D. D. Holm, E. Luesink and W. Pan, Stochastic mesoscale circulation dynamics in the thermal ocean, Phys. Fluids33 (2021) 046603, https://doi.org/10.1063/5.0040026 ]. [ABSTRACT FROM AUTHOR]

In this paper, Myc/E2F/miR-17-92 network under Gaussian white noise is studied. Taking the time delay as the parameter, the Hopf bifurcation of the system is obtained, which causes the protein concentration to oscillate periodically. Under the influence of time delay and noise, the stochastic D-bifurcation of the system is obtained. It is worth noting that the occurrence of stochastic P-bifurcation is successfully captured. Thus a pattern of coexistence of high and low protein concentrations is founded in the network. The specific research methods of this paper are as follows: firstly, the system is reduced to a finite dimensional system by using stochastic center manifold and normal form theory. Then, using the stochastic averaging method, the Fokker–Planck–Kolmogorov equation of the system is constructed in which the statistical response in the stationary state is the probability density. Finally, the stochastic bifurcation analysis and numerical simulation are carried out. The agreements between the analytical method and those obtained numerically validate the effectiveness of the analytical investigations. [ABSTRACT FROM AUTHOR]

An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such a perturbative amplitude is related to many important physical process treated in the Standard Model context. The background of this investigation is an alternative strategy to handle the divergences typical for perturbative solutions of quantum field theory. Since its proposition, the mentioned method was exhaustively used to calculate and manipulate one-loop Feynman integrals with a great success. However, the great advances in precision of experimental data collected in particle physics colliders have pushed up theoretical physicists to improve their predictions through multi-loop calculations. In this paper, we describe the main steps required to perform two-loop calculations within the context of the referred method. We show that the same rules used for one-loop calculations are enough to deal with two-loop graphs as well. Analytic results for the sunrise graph are obtained in terms of elliptic multiple polylogarithms as well as a numerical analysis is provided. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of a predator–prey system of an ecological community in which the fear instigated by the predators has an adverse effect on the reproduction rate of prey species, and also on the competition among themselves due to the limited environmental resources. To capture and handle the realistic scenario in a more meaningful way, we have mathematically built up the model system with the assumption that the predators predate on the prey items following Cosner functional response, which increases with increments in the prey and predator populations. The model system has been studied through noteworthy mathematical analysis and an extensive numerical simulation. Our simulation results demonstrate that the predator–prey system stabilizes due to predator's induced fear suppressing/enhancing the birth/death of prey species. The competition among the predators for the available prey items also has a stabilizing role on the system's dynamics. In contrast, the increasing growth rate of prey species or predation rate creates instability in the system by changing the stable phase to the limit cycle oscillations. Moreover, the effects of seasonality are also studied by extending the model system to its nonautonomous counterpart. Sufficient conditions are derived so that the seasonally driven system exhibits at least one positive periodic solution. Our numerical results show that the seasonally forced system exhibits periodic solution (globally attractive periodic solution), higher periodic solutions, bursting patterns and the extinction of predator species due to the seasonal variations of some parameters. [ABSTRACT FROM AUTHOR]

The P53 protein levels exhibit a series of pulses in response to DNA double-stranded breaks (DSBs). However, the mechanism regarding how damage strength regulates physical parameters of p53 pulses remains to be elucidated. This paper established two mathematical models translating the mechanism of p53 dynamics in response to DSBs; the two models can reproduce many results observed in the experiments. Based on the models, numerical analysis suggested that the interval between pulses increases as the damage strength decreases, and we proposed that the p53 dynamical system in response to DSBs is modulated by frequency. Next, we found that the ATM positive self-feedback can realize the system characteristic that the pulse amplitude is independent of the damage strength. In addition, the pulse interval is negatively correlated with apoptosis; the greater the damage strength, the smaller the pulse interval, the faster the p53 accumulation rate, and the cells are more susceptible to apoptosis. These findings advance our understanding of the mechanism of p53 dynamical response and give new insights for experiments to probe the dynamics of p53 signaling. [ABSTRACT FROM AUTHOR]

This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor. [ABSTRACT FROM AUTHOR]

Hidden chaotic attractors is a fascinating subject of study in the field of nonlinear dynamics. Jerk systems with a stable equilibrium may produce hidden chaotic attractors. This paper seeks to enhance our understanding of hidden chaotic dynamics in jerk systems of three variables (x , y , z) with nonlinear terms from a predefined set: { − x y + d z 2 , − x y + d z tanh (z) } , where d is a real parameter. The behavior of the systems is analyzed using rigorous Hopf bifurcation analysis and numerical simulations, including phase portraits, bifurcation diagrams, Lyapunov spectra, and basins of attraction. For certain jerk systems with a subcritical Hopf bifurcation, adjusting the coefficient of a linear term can lead to hidden chaotic behavior. The adjustment modifies the subcritical Hopf equilibrium, transforming it from an unstable state to a stable one. One such jerk system, while maintaining its equilibrium stability, experiences a sudden transition from a point attractor to a stable limit cycle. The latter undergoes a period-doubling route to chaos, which may be followed by a reverse route. Therefore, by perturbing certain jerk systems with a subcritical Hopf equilibrium, we can gain insights into the formation of hidden chaotic attractors. Furthermore, adjusting the coefficient of the nonlinear term z tanh (z) in certain systems with a stable equilibrium can also lead to period-doubling routes or reverse period-doubling routes to hidden chaotic dynamics. Both findings are significant for our understanding of the hidden chaotic dynamics that can emerge from nonlinear systems with a stable equilibrium. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solution of the time-fractional Gilson–Pickering equation using the Kansa method, in which the multiquadrics were utilized as the radial basis function. To achieve this, a meshless numerical scheme based on the finite difference along with the Kansa method has been presented. First, the finite difference approach has been utilized to discretize the temporal derivative, and subsequently, the Kansa method is employed to discretize the spatial derivatives. The stability and convergence analysis of the numerical scheme are also elucidated in this paper. Furthermore, the soliton solutions have been acquired by implementing the Kudryashov method for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, two different types of plasma models with variable coefficients are described by using the fractal derivative. This paper aims at establishing fractal variational principles for two different types of discontinuous plasma physics by the fractal semi-inverse method, so that it can be applied to numerical analysis of the effect of the discontinuous time and discontinuous space on the solution properties. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear dynamical behaviors of a time-delayed supercavitating vehicle system varying with the system parameters, and proposes control strategies to stabilize the trajectory. A simplified dynamical model of the supercavitating vehicle is firstly constructed and then analyzed on its local and global stability in terms of different parameter values and initial conditions. Due to the forces resulting from the fins and the afterbody plane causing one of the system parameters to become a piecewise constant function of position, the system is described as a linear switched one with time delay. Both theoretical analysis and numerical simulations are adopted to describe the system behaviors. Several special phenomena such as bifurcations, deviation behaviors and period-doubling processes emerging from the system for a given set of parameters are discussed in detail in this paper. Besides, the equilibrium and chaotic solutions are accurately located by plotting the Lyapunov exponent map. Chaotic attractors present different strange forms with the variation of the parameters. Finally, based on the system's global property, the control and anti-control strategies are proposed to stabilize the system or generate desirable chaos and it is shown that the system can be controlled by selecting appropriate control parameters. [ABSTRACT FROM AUTHOR]

This paper introduces a new 3D conservative chaotic system. The oscillator preserves the energy over time, according to the Kaplan–Yorke dimension computation. It has a line of unstable equilibrium points that are investigated with the help of eigenvalues and also numerical analysis. The bifurcation diagrams and the corresponding Lyapunov exponents show various behaviors, for example, chaos, limit cycle, and torus with different parameters. Other dynamical properties, such as Poincaré section and basin of attraction, are investigated. Additionally, an oscillator's electrical circuit is designed and implemented to demonstrate its potentiality. [ABSTRACT FROM AUTHOR]

In this research paper, we find the numerical solutions of fractional order scalers and coupled system of differential equations under initial conditions using shifted Legendre polynomials. By using the properties of shifted Legendre polynomials, we establish operational matrices of integration and differentiation in order to simplify our considered problems under initial conditions. In order to check the accuracy of the proposed model, some test problems are solved along with the graphical representations. For coupled system, we applied the algorithm to the Pharmacokinetic two-compartment model. As the proposed method is computer-oriented, we use therefore the MATLAB for required calculations. Numerical results are shown graphically. [ABSTRACT FROM AUTHOR]

In this paper, the Melnikov method for an abstract stochastic nonsmooth hybrid system is derived in detail and employed to study the homoclinic bifurcations and induced chaos in a bistable vibro-impact SD oscillator with bounded noise first proposed by Li et al. 2021, in which the geometric nonlinearity is used to produce the irrational restoring force and an impact map is introduced to describe energy loss during collisions. The initial Poincaré section is selected on the right rigid constraint so that rigorous perturbation analysis can be carried out to avoid the extension of trajectories near the switching manifold. The stochastic Melnikov function with geometrical intuition is obtained to detect the threshold of parameters for homocinic tangency of the perturbed stochastic stable and unstable manifolds by calculating the energy difference of their initial points on the Poincaré section. Finally, the analytical Melnikov analysis combined with numerical simulations is carried out to validate the developed Melnikov method for analyzing the global dynamics of the bistable vibro-impact SD oscillator subject to bounded noise. [ABSTRACT FROM AUTHOR]

The assembled tube-gusset K-joint by bolts is a commonly used connection form in steel tubular transmission towers. At present, main existing research or design codes for steel tubular transmission towers regard this K-joint as either rigid or pinned connections, which do not consider the semi-rigid behavior of K-joint. In this paper, the semi-rigid behavior of K-joint in steel tubular transmission towers is investigated and a direct prediction (DP) method is proposed to evaluate the semi-rigid behavior of K-joints based on the support vector regression (SVR) model, especially to predict the moment–rotation curve of semi-rigid K-joints. First, the establishment and validation of the finite element (FE) model of semi-rigid K-joints are conducted. Second, a dataset of 144 samples generated by the FE model is used to train and test the SVR model. Finally, the accuracy assessment of the proposed DP method and comparison with other existing methods, including the Kishi–Chen model, EC3 model and ANN-based two-step prediction method, are presented. The accuracy assessment shows that predicted values of the proposed DP method based on the SVR model exhibit good agreement with the numerical analysis values, which indicates the quite high accuracy of this method. Additionally, the comparison reveals that the proposed DP method based on the SVR model for predicting moment–rotation curves is rather more accurate than other aforementioned methods. Therefore, the proposed DP method based on the SVR model is of high reliability in predicting the semi-rigid behavior of K-joints in steel tubular transmission towers, which affords an alternative way for further engineering analysis and initial design purposes. [ABSTRACT FROM AUTHOR]

In this paper, a novel dual-band monopole planar antenna is presented. The antenna is operated in 28/38 GHz and has a bandwidth of 0.5/0.7 GHz to operate in 5G frequency bands. Additionally, it exhibits a stable omni-directional radiation pattern with high gain characteristics, which helps to improve the performance of future 5G communication devices. The radiation efficiency achieved more than 94% throughout its operating bands. The numerical analysis has been carried out using a three-dimensional (3D) full-wave electromagnetic solver (ANSYS HFSS). In order to validate the numerical analysis, the proposed antenna has been fabricated and shows a good agreement with simulated results. The antenna has been designed and fabricated on Roger RT/Duroid 5880 dielectric substrate. This paper paves a new idea to design dual-band, simple and miniaturized single-element monopole planar antennas, which would be a good candidate for future millimeter-wave 5G communication systems. [ABSTRACT FROM AUTHOR]

This paper addresses the numerical study of variable-order fractional differential equation based on finite-difference method. We utilize the implicit numerical scheme to find out the solution of two-dimensional variable-order fractional modified sub-diffusion equation. The discretized form of the variable-order Riemann–Liouville differential operator is used for the fractional variable-order differential operator. The theoretical analysis including for stability and convergence is made by the von Neumann method. The analysis confirmed that the proposed scheme is unconditionally stable and convergent. Numerical simulation results are given to validate the theoretical analysis as well as demonstrate the accuracy and efficiency of the implicit scheme. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical and complex numerical analysis of the 2-torus chaotic system with a power-law kernel. Various dynamical characteristics of the complex system are investigated covering existence uniqueness, attractor projection, time series analysis and sensitivity towards initial values. 4-torus attractor coexistence is observed with different fractional orders. The numerical scheme is used to approximate the system numerically which is based on the Newton polynomials. The numerical illustrations of the system demonstrate that moving from higher fractional-order to lower fractional-order affects the dynamics of the system significantly, which in turn has a shrinking impact on the geometry of the oscillatory range. The emergence of new oscillations can also be observed at lower fractional orders, revealing that the system oscillates rapidly with lower amplitudes as compared to those having higher fractional orders. [ABSTRACT FROM AUTHOR]

Magnetically Mediated Thermoacoustic Imaging (MMTAI) is a new imaging technology that uses the thermoacoustic effect of electromagnetic fields. It is capable of a high resolution in ultrasonic imaging and high contrast in electrical impedance imaging. It has considerable potential applications in the early diagnosis of diseases. First, this paper describes the theoretical analysis and numerical simulation of MMTAI. For B-scan thermoacoustic imaging, the thermoacoustic image of a two-dimensional model is simulated and analyzed. The numerical simulation results provide theoretical guidance for the design of the experiment. Second, the B-scan experimental system of MMTAI is designed and built. The imaging experiment was carried out using an imitation gel that contains sodium chloride as the target, and the imaging results were basically consistent with the conductivity distribution of the target. Numerical simulation and physical experiments verify the feasibility of the MMTAI method for low conductivity media. This preliminary study has shown the feasibility of the technique to detect conductivity boundaries, making it relevant for the future application of this method in the field of biomedical imaging. [ABSTRACT FROM AUTHOR]

In this paper, a novel underdamped tri-stable stochastic resonance (NUTSR) is presented in order to overcome the low out-performance of weak signal reinforcement in the classical tri-stable stochastic resonance (CTSR). The two systems are compared using the input and output amplitude as a measure when noiseless. NUTSR improves the output saturation characteristics and has more outstanding signal enhancement capability. In the background of Gaussian noise, the expressions of mean first-pass time (MFPT), steady-state probability density (SPD) and signal-to-noise ratio (SNR) are derived. The fourth-order Runge–Kutta algorithm and genetic algorithm (GA) is used for numerical simulations. Then the numerical simulation results of the two systems are compared comprehensively, and the theoretical deduction and numerical simulation results of NUTSR are also compared. Moreover, the two systems are applied in two bearing fault types of 6205-2RS JEM SKF and HRB 6205-2Z. Finally, the feasibility of NUTSR is verified under different noise, which is simulated numerically under symmetric trichotomous that NUTSR has better noise immunity and the increase in signal amplitude is more pronounced. [ABSTRACT FROM AUTHOR]

In this paper, the concept of hyperneuron is introduced. The main properties and dynamical characteristics of this class of hypersystems will be studied by numerical analysis. The intrinsic robustness of the proposed model is further investigated by proposing a silicon implementation of the hyperneuron, reporting the corresponding experimental results. The study aims to present a novel approach to in silico implementations of large-scale networks of neurons with increased robustness and fault tolerance. [ABSTRACT FROM AUTHOR]

Cellular automaton (CA) as a discrete and deterministic dynamic system has been widely used in cryptography. In this paper, a novel triple-coupling CA model is proposed. We first apply the triple-coupling model to 1D CA to design a high-quality pseudo-random number generator (PRNG). Numerical simulation and analyses show that triple-coupling CA exhibits more complex evolutionary behavior than uncoupling CA. The pseudo-random sequence generated by triple-coupling 1D CA can pass all NIST SP800-22 tests. Subsequently, the triple-coupling model is also applied to 2D CA, and a novel image encryption scheme based on this model is proposed. Thanks to the triple-coupling model, the diffusion operation can be completed between different color channels of the color image. Experimental simulations and extensive cryptanalysis show that the image encryption algorithm using the triple-coupling model has superior security and high efficiency. [ABSTRACT FROM AUTHOR]

The implicit frequency dependence of linear systems arising from the acoustic boundary element method necessitates an efficient treatment for problems in a frequency range. Instead of solving the linear systems independently at each frequency point, this paper is concerned with solving them simultaneously at multiple frequency points within a single iteration scheme. The proposed concept is based on truncation of the frequency range solution and is incorporated into two well-known iterative solvers - BiCGstab and GMRes. The proposed method is applied to two acoustic interior problems as well as to an exterior problem in order to assess the underlying approximations and to study the convergence behavior. While this paper provides the proof of concept, its application to large-scale acoustic problems necessitates efficient preconditioning for multi-frequency systems, which are yet to be developed. [ABSTRACT FROM AUTHOR]

This paper is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuška–Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular, examples of limit load problems and similar ones arising in classical plasticity, gradient plasticity and delamination are introduced. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Filippov switching model which is composed of the Lorenz and Chen systems. By employing the qualitative analysis techniques of nonsmooth dynamical systems, we show that the new Filippov system not only inherits the properties of the Lorenz and Chen systems but also presents new dynamics including new chaotic attractors such as four-wing butterfly attractor, Lorenz attractor with sliding segments, etc. In particular, we find that different new attractors can coexist such as the coexistence of two-point attractors and chaotic attractor, the coexistence of two-point attractors and quasi-periodic solution, the coexistence of transient transition chaos and quasi-periodic solution. Furthermore, nonsmooth bifurcations and numerical analyses reveal that the proposed Filippov system has a series of new sliding bifurcations including a symmetric pair of sliding mode bifurcations, a symmetric pair of sliding Hopf bifurcations, and a symmetric pair of Hopf-like boundary equilibrium bifurcations. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic model given by three-dimensional ordinary differential equations is studied to determine how the dynamics of tumor growth is controlled by some key parameters. By varying the competition coefficient between healthy host cells and tumor cells, a Hopf bifurcation occurs in this system, leading to the creation of a stable limit cycle. Through numerical analysis of the continuity of this limit cycle, we find that the cascade of period-doubling bifurcations leads to the generation of a chaotic attractor. Moreover, the region of attractors is shown in the parameter space. Numerical simulations, bifurcation diagrams, Lyapunov exponent graph and phase portraits permit to highlight the rich and complex phenomena presented by the model. [ABSTRACT FROM AUTHOR]

Modern factory automation is enabling the economic production of timber building components with sophisticated integral mechanical joints. This paper investigates the governing compressive failure mechanisms of full-length integrally-jointed plywood box columns, and in particular seeks to understand the interaction between localized material knot defects, integral box joint capacity, and column strength. A new critical failure mechanism is identified based on experimental observations and numerical analysis of sections with varying sizes of knot defect, with column capacity governed by defect-induced transverse loading of integral box joints. Column capacity was shown to improve with localized joint strengthening in knot-defective regions, or with a defect-adaptive fabrication procedure that avoids identified defects during component plate machining. The new failure mechanism was also combined with prior understanding of plate buckling and pop-off failure mechanisms to propose an overall failure process for integrally-jointed plywood columns. Results from this paper can also inform development of other types of integrally-jointed thin-walled structures. [ABSTRACT FROM AUTHOR]

Initial condition-dominated offset boosting provides a special channel for coexisting orbits. Due to the nonlinearity and inherent periodicity, sinusoidal function is often introduced into a dynamical system for multistability design. Typically, the distance between two attractors or two petals of an attractor is fixed. Moreover, any chaotic signal and sequence need to be modified with amplitude and offset for a real application. In this paper, an initially-controlled double-scroll hyperchaotic map is constructed based on two sine functions. Four patterns of the double-scroll hyperchaotic orbits are found as 0-degree, 90-degree, 45-degree and 135-degree. Consequently, different modes for attractor growing are demonstrated. In this case, all the coexisting attractors are arranged in phase space in a direction defined by the initial value and the distance between two petals of any double-scroll orbit is adjusted. Finally, hardware experiments based on STM32 are carried out to verify the theoretical analysis and numerical simulation. [ABSTRACT FROM AUTHOR]

The review focuses on three main essentials of numerical analyses, namely soil behavior and constitutive model, pile and pile-soil interface modeling and computational framework. This paper presents a critical review of the current challenges in analyzing large, realistic pile groups in soft clay soil under earthquake shaking. [Extracted from the article]

This paper elucidates the bifurcation mechanism of an equidistant economy in spatial economics. To this end, we derive the rules of secondary and further bifurcations as a major theoretical contribution of this paper. Then we combine them with pre-existing results of direct bifurcation of the symmetric group S N [Elmhirst, 2004]. Particular attention is devoted to the existence of invariant solutions which retain their spatial distributions when the value of the bifurcation parameter changes. Invariant patterns of an equidistant economy under the replicator dynamics are obtained. The mechanism of bifurcations from these patterns is elucidated. The stability of bifurcating branches is analyzed to demonstrate that most of them are unstable immediately after bifurcation. Numerical analysis of spatial economic models confirms that almost all bifurcating branches are unstable. Direct bifurcating curves connect the curves of invariant solutions, thereby creating a mesh-like network, which appears as threads of warp and weft. The theoretical bifurcation mechanism and numerical examples of networks advanced herein might be of great assistance in the study of spatial economics. [ABSTRACT FROM AUTHOR]

Based on big data, this paper starts from the behavior data of users on social media, and studies and explores the core issues of user modeling under personalized services. Focusing on the goal of user interest modeling, this paper proposes corresponding improvement measures for the existing interest model, which has great difference in interest description among different users and it is difficult to find the user interest change in time. For the above problems, this paper takes user-generated content and user behavior information as the analysis object, and uses natural language processing, knowledge warehouse, data fusion and other methods and techniques to numerically analyze user interest mining based on text mining and multi-source data fusion. We propose a user interest label space mapping method to avoid data sparse problem caused by too many dimensions in interest analysis. At the same time, we propose a method to extract and blend the long-term and short-term interests, and realize the comprehensive evaluation of interests. In the analysis of the big data phase, the user preference social property application preference value law, it is expected to achieve user Internet social media application preference data mining from the perspective of big data. [ABSTRACT FROM AUTHOR]