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In this study, control and fault detection are examined for Takagi–Sugeno (T–S) fuzzy continuous-time systems with conic-type nonlinearity. In a conic-type dynamic system, Takagi–Sugeno fuzzy models are applied. A conic-type non-linearity must lie in an n-dimensional hyper-sphere with an uncertain centre to satisfy the restrictive condition. A combined error system of estimation and control error is obtained by combining the observations and the controller. Our main goal is to design an observer and controller for fault detection that minimizes the impact of unknown inputs and faults on the system in terms of the $ H_{\infty } $ H ∞ performance. The Lyapunov function is used to construct the residual signal using an observer and a controller. Using Linear Matrix Inequalities (LMIs), we can express the performance conditions for $ H_{\infty } $ H ∞ . The scheme's effectiveness is demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

This primer article focuses on the existence, uniqueness and Ulams stability of semilinear nonautonomous dynamic problem with impulses on time scales, by utilizing fixed point method. We establish our results with the help of abstract Grönwall inequality and Picard operator. We utilize some assertions to overcome difficulties. To demonstrate our main result, we provide an example at the end. [ABSTRACT FROM AUTHOR]

In this work, a novel approach for the reliable and efficient numerical integration of the Kuramoto model on graphs is studied. For this purpose, the notion of order parameters is revisited for the classical Kuramoto model describing all-to-all interactions of a set of oscillators. First numerical experiments confirm that the precomputation of certain sums significantly reduces the computational cost for the evaluation of the right-hand side and hence enables the simulation of high-dimensional systems. In order to design numerical integration methods that are favourable in the context of related dynamical systems on network graphs, the concept of localized order parameters is proposed. In addition, the detection of communities for a complex graph and the transformation of the underlying adjacency matrix to block structure is an essential component for further improvement. It is demonstrated that for a submatrix comprising relatively few coefficients equal to zero, the precomputation of sums is advantageous, whereas straightforward summation is appropriate in the complementary case. Concluding theoretical considerations and numerical comparisons show that the strategy of combining effective community detection algorithms with the localization of order parameters potentially reduces the computation time by several orders of magnitude. [ABSTRACT FROM AUTHOR]

In this paper, we construct and analyze explicit nonstandard Runge-Kutta (ENRK) methods which have higher accuracy order and preserve two important properties of autonomous dynamical systems, namely, the positivity and linear stability. These methods are based on the classical explicit Runge-Kutta methods, where instead of the usual h in the formulas there stands an appropriately chosen function φ (h). It is proved that the constructed methods preserve the accuracy order of the original Runge-Kutta methods. Some performed numerical simulations confirm the validity of the obtained theoretical results as well as the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems of equations, which are predominantly dependent on slowly varying parameter values. We focus on efficiently solving these linear systems, specifically those arising in a set of algorithms for reducing linear dynamical systems with the parameters linearly embedded in the system matrices. We propose the use of the block variant of the problem-dependent underlying iterative method because often, all right hand sides are available together. Since Sparse Approximate Inverse (SPAI) preconditioner is a general preconditioner that can be naturally parallelized, we propose its use. Our most novel contribution is a technique to cheaply update the SPAI preconditioner, while solving parametrically changing linear systems. We support our proposed theory by numerical experiments where-in two different models are reduced by a commonly used parametric model order reduction algorithm called RPMOR. Experimentally, we demonstrate that using a block variant of the underlying iterative solver saves nearly 95% of the computation time over the non-block version. Further, and more importantly, block GCRO with SPAI update saves around 60% of the time over block GCRO with SPAI. [ABSTRACT FROM AUTHOR]

The 0–1 test for chaos is increasingly used in applications where it is important to distinguish between chaotic and regular dynamics of the deterministic dynamical system. This test consists of translating the time series into (p , q) plane. Then the boundedness of the object created in the (p , q) plane is inspected by computing mean square displacement and its growth rate. The computation of the mean square displacement for various lag has high computational complexity. In this paper, the inspection of the boundedness using bounding box and centre of gravity is proposed. This method has linear computational complexity and provides more control over the precision of the test through multiple input parameters. [ABSTRACT FROM AUTHOR]

In this article, we show how to determine attractors in sequential dynamical systems on maxterm and minterm Boolean functions and their corresponding basins of attraction. Furthermore, we make possible to know when an attractor is globally attractive. As the main result of this work, upper bounds for the transient in such models are provided. In order to do that, we distinguish two possible scenarios: fixed point sequential dynamical systems and periodic orbit sequential dynamical systems. [ABSTRACT FROM AUTHOR]

We formulate a deterministic mathematical model for the dynamical transmission of Neisseria meningitidis serogroup A (NmA) within a community. The model incorporates the key epidemiological and biological features ofNmAsuch as the vaccine efficacy and the waning of both vaccine-induced and recovery-induced immunity . We provide a theoretical study of the model. We compute the disease-free equilibrium (DFE) and derive the basic reproduction numberthat determines the extinction and the persistence of the disease. We compute equilibria and study their stability. More precisely, we show that there exists a threshold parameterξsuch that when, the DFE is globally asymptotically stable while when, the model exhibits the phenomenon of backward bifurcation on a feasible region. We also investigate the impact of imperfect mass vaccination with waning immunity within a community. The theory is supported by numerical simulations, which further suggest that the control of the epidemic ofNmApass through a combination of a large coverage vaccination of young susceptible individuals and the production of a vaccine with a high level of efficacy. Sensitivity analysis of the model has been performed in order to determine the impact of related parameters on meningitis outbreak. [ABSTRACT FROM PUBLISHER]

A new dynamic system is proposed and investigated for solving online simultaneous linear equations. Compared with the gradient-based dynamic system and the recently proposed Zhang dynamic system, the proposed dynamic system can achieve superior convergence performance (i.e. finite-time convergence) and thus is called the finite-time convergent dynamic system. In addition, the upper bound of the convergence time is derived analytically with the error bound being zero theoretically. Simulation results further indicate that the proposed dynamic system is much more efficient than the existing dynamic systems. [ABSTRACT FROM AUTHOR]

Many dynamical systems in physics and engineering are characterized by the property of possessing a bounded absorbing set which all trajectories enter in a finite time and thereafter remain inside. It is highly important to analyse whether or not the numerical methods for solving these dynamical systems inherit such property of the underlying systems. In this paper, it is proved that, under some assumptions, a multistep Runge–Kutta (abbrev. MRK) method is dissipative when it is applied to a class of neutral integro-differential equations with delay, provided it is-algebraically stable. Numerical examples are given to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

We study the phenomenon of slow convergence in families of discrete dynamical systems where the iteration function has a Puiseux series representation. Such occurrence consists in the slow convergence of orbits near non-hyperbolic parametric periodic points. We provide a precise new definition of the slowness of convergence which is based on literature results for the critical exponents associated with parametric periodic points. Such exponents establish a general classification for slow systems and provide a measure of rates of convergence. For dynamical systems whose iteration functions have Taylor series expansions, the new definition is natural with wider applicability. However, it can be also used for iteration functions where a more sophisticated approach, such as a Lagrange expansion, is needed. In addition, we show that even for such iteration functions, the critical exponent can be easily computed. The presented theoretical results are illustrated by numerical examples having different rates of convergence. [ABSTRACT FROM AUTHOR]

Compared with traditional online social networks (OSNs), mobile OSNs (mOSNs) take a step further in that they provide the location-based services, and location-sharing is a fundamental component of mOSN. However, without privacy protection, users may be hesitant to share their locations. In this paper, we present a new privacy-preserving location-sharing system for mOSN, which is flexible to support a variety of location-based applications, in that it enables location-sharing between both trusted social relations and untrusted strangers. It allows user to dynamically change his sharing decryption key when to add or revoke a friend. We further propose a security improved system, which can be secure against neighborhood attacks. In our proposed systems, threat models are further analysed and users’ location privacy is proved secure. Implementation and evaluation show that they are efficient and practical. [ABSTRACT FROM AUTHOR]

In this paper, we consider the modelling and identification in the fed-batch fermentation of glycerol byKlebsiella pneumoniaewith open-loop glycerol input and pH logic control. Taking into account the hybrid characteristic of the fed-batch operation, we present a nonlinear hybrid dynamical system, which is developed by embedding the discrete process of adding glycerol and alkali into the dynamical system of batch culture, to formulate this fermentation process. Some important properties of the solution to the proposed system are then discussed, including the existence, uniqueness, boundedness and regularity. To estimate the unknown parameters in the system, a parameter identification problem subject to continuous state inequality constraints is proposed, and its identifiability is also proved. Subsequently, the parametric sensitivity functions of the system are given and utilized to obtain the requisite gradient information for further numerical computation. Finally, to solve the identification problem, a gradient-based algorithm is constructed in conjunction with constraint transcription and the smoothing approximation technique. Numerical simulations show that the validated hybrid system is fit for describing the fed-batch processes as observed from the experimental results. [ABSTRACT FROM AUTHOR]

By analysing spot price characteristics at compliance time from equilibrium perspective, the COprice dynamical models are obtained for both bankable and nonbankable regulations with the prices of spots and futures being non-log-normal, and the futures option pricing model is established. Then, a fitted finite volume method (FVM) is proposed to solve the pricing model. Also, its monotonicity, stability, and convergence are studied. Furthermore, the convergence rates are compared between our fitted FVM and the finite difference method. Moreover, the Δ-hedge experiments are performed, in which the hedge cost and the hedge error are estimated. Finally, using the Monte Carlo's pricing results as a benchmark, we compare the computational results from the fitted FVM and the Black formula approximation, respectively, which shows that the former is fitted for the Monte Carlo better than the latter, especially for the futures options with the bigger volatility or the maturity near the compliance time. [ABSTRACT FROM PUBLISHER]

The performances of jump-risk mitigation under a double Heston stochastic volatility jump-diffusion (dbHJ) model are examined. The quadratic exponential (QE) scheme is used to simulate the-measure price paths supposed to follow the dbHJ model, whereas a Fourier-COS-expansion-based scheme (i.e. the COS formula, see [F. Fang and C.W. Oosterlee,A novel pricing method for European based on Fourier-cosine series expansions, SIAM J. Sci. Comput. 31 (2008), pp. 826–848] is employed to price options and to calculate Greeks. Numerical results from extensive dynamic hedging experiments suggest that, when facing a-measure market with stiff volatility skews and non-trivial jumps, the dbHJ model is better than the plain (double) Heston and Black–Scholes models, and slightly outperforms the Heston stochastic volatility jump-diffusion (HJ) model and the Merton model in mitigating the jump risk of an option. This conclusion holds independent of the model specification of-measure market. [ABSTRACT FROM PUBLISHER]

In this paper we design, by using the weight function technique, two families of iterative schemes with order of convergence eight. These weight functions depend on one, two and three variables and they are used in the second and third step of the iterative expression. Dynamics on polynomial and non-polynomial functions is analysed and they are applied on the problem of preliminary orbit determination by using a modified Gauss method. Finally, some standard test functions are to check the reliability of the proposed schemes and allow us to compare them with other known methods. [ABSTRACT FROM PUBLISHER]

Stochastic and deterministic versions of a discrete dynamical system on a necklace are investigated. This network consists of a sequence of contoursNSWEwith nodes, i.e. the nodes are common points atWandE. There are two cells and a particle on each contour. Each time instance, the particle occupies a cell and, at every time unit, comes to the next cell in the same direction. The particles of the neighbouring contours move in accordance with rules of stochastic or deterministic type. The behaviour of the model with the rule of the first type is stochastic only at the beginning and after a time interval becomes a pure deterministic system. The system with the second rule comes to a steady mode, which depends on the initial state. The average velocity of particles and characteristics of the system are studied. [ABSTRACT FROM PUBLISHER]

In this paper, the dynamics of the family of c-iterative methods for solving nonlinear equations are studied on quadratic polynomials. A singular parameter space is presented to show the complexity of the family. The analysis of the parameter space allows us to find elements of the family that have bad convergence properties and also other ones with very stable behaviour. These schemes correspond to values ofcin different small regions of the parameter space. [ABSTRACT FROM PUBLISHER]

In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This situation is rather common especially in population dynamics models, like prey–predator or competition systems. Focusing on squirrels population models with niche, in this paper we design algorithms for the detection and the refinement of points lying on the separatrix manifold partitioning the phase space. We consider both the two populations and the three populations cases. To reconstruct the separatrix curve and surface, we apply the Partition of Unity method, which makes use of Wendland's functions as local approximants. [ABSTRACT FROM PUBLISHER]

This article analyses a mode of two-dimensional fox-rabies dynamics with advection terms. The fox population is divided into two species: susceptible S and infective I. Finite-difference techniques are employed to compute the numerical solutions of this model. Iterative schemes with second-order accuracy are derived and their convergence is investigated by using the maximum principle analysis. An illustrative numerical example with graphical reis given to highlight the efficiency of the derived numerical schemes. [ABSTRACT FROM PUBLISHER]

In this article, we provide a matrix method in order to compute orbits of parallel and sequential dynamical systems on Boolean functions. In this sense, we develop algorithms for systems defined over directed (and undirected) graphs when the evolution operator is a general minterm or maxterm and, likewise, when it is constituted by independent local Boolean functions, so providing a new tool for the study of orbits of these dynamical systems. [ABSTRACT FROM AUTHOR]

A special kind of neural dynamics, termed Zhang dynamics (ZD), is proposed, generalized and investigated for the online solution of time-varying scalar-valued nonlinear inequalities by following Zhanget al.’s design method. The continuous-time ZD (CTZD) model based on an exponent-type design formula can be guaranteed to exponentially converge to the time-varying solution set of the problem in an error-free manner. For potential hardware implementation on digital circuits, the corresponding discrete-time ZD (DTZD) model is generated through the well-known Euler forward difference rule. Newton-type algorithm is also developed for comparison purposes. In addition, the simplified CTZD (S-CTZD) and DTZD (S-DTZD) models are developed for solving static scalar-valued nonlinear inequalities. Numerical simulative examples further demonstrate and verify the efficacy of the ZD models for solving time-varying and static scalar-valued nonlinear inequalities. Besides, the DTZD model possesses the lower complexity and higher accuracy, as compared with the Newton-type algorithm. [ABSTRACT FROM AUTHOR]

Metabolic P (MP) grammars are a particular class of multiset rewriting grammars introduced in the MP theory for modelling metabolic processes. In this paper, a new algebraic formulation of inverse problems, based on MP grammars and Kronecker product, is given, for further motivating the correctness of the LGSS (Log-Gain Stoichiometric Stepwise) algorithm, introduced in 2010s for solving inverse problems in the MP framework. At the end of the paper, a section is included that introduces the problem of multicollinearity, which could arise during the execution of LGSS, and that defines an algorithm, based on a hierarchical clustering technique, that solves it in a suitable way. [ABSTRACT FROM PUBLISHER]

Rule 110 is a complex cellular automaton (CA) in Wolfram's system of identification, capable of supporting universal computation. It has been suggested that a universal CA should be on the 'edge of chaos', which means that the dynamical behaviour of such a system is neither simple nor chaotic. There is no doubt that the dynamical property of Rule 110 is extremely complex and still not well understood. This paper proves the existence of subsystems on which this rule is chaotic in the sense of Devaney. [ABSTRACT FROM AUTHOR]

In this paper, we consider an ecosystem in which two disease-affected populations thrive and in which the epidemics can spread from one species to the other one by contact. The feasibility and stability conditions of the equilibria of the system are investigated analytically. The model does not possess Hopf bifurcations. Numerical simulations are performed to investigate the role of the main epidemiological and demographic parameters in the model, thus discovering that the predation of healthy or diseased predators on an infected prey allows some kind of control of the prey, if the latter, for instance, represents a pest. [ABSTRACT FROM PUBLISHER]

Conjugate gradient method is a root-finding algorithm to non-linear equations. In this paper, we suggest extending this method for a polynomial to the complex plane. Through the experimental and theoretical mathematics method, we drew the following conclusions: (1) the conjugate gradient is a dynamical system with two complex parameters; (2) locally conditions for convergence to any roots of complex functions is given; (3) the conjugate gradient method may fail to converge to all roots for cubic with three simple roots; (4) the boundary of conjugate gradient basins are fractals in some cases, and depends on the parameters; (5) the algorithm is then improved by introducing a method to determine the optimal parameters. [ABSTRACT FROM AUTHOR]

In this paper, we present a structure-preserving model-order reduction method for solving large-scale second-order MIMO dynamical systems. It is a projection method based on a block second-order Krylov subspace. We use the block second-order Arnoldi (BSOAR) method to generate an orthonormal basis of the projection subspace. The reduced system preserves the second-order structure of the original system. Some theoretical results are given. Numerical experiments report the effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this paper the deterministic manner of complex systems from which a time series of one variable is known, is investigated by the use of neural networks. The idea on which the method is based is that back propagation neural networks with sigmoid nodes can simulate deterministic systems. This means that when a neural network is able to learn a system successfully, the system is deterministic, but when it is not, no such statement can be directly asserted. In this case simple criteria are proposed, presuming that when the proper amount of information feeds the network its performance is improved. This improvement indicates the network's effort to capture, in some way, the deterministic properties of the simulated system. This consideration is confirmed by the observation that random systems do not satisfy any of the criteria proposed in this work. The neural method of investigating determinism is simpler than methods proposed in previous research work, since no pre-calculated parameter values, such as the delay time or the embedding dimension of the dynamical system, are necessary for its implementation. [ABSTRACT FROM AUTHOR]

This article discusses various aspects of neural modeling of multidimensional chaotic attractors. The Lorenz and Rosler attractors are considered as representative cases and are thoroughly examined. These two dynamical systems are expressed, within acceptable accuracy limits, by the corresponding systems of difference equations. Initially, the complete neural models of the attractors are examined. In this case, the neural networks are supplied with the values X n , Y n , Z n of the systems to predict all the next components ( X n +1 , Y n +1 , and Z n +1 ) of the attractors. In the second case, named 'component simulation', the neural models are trained to predict only one of the values X n , Y n , Z n , when they are fed with the complete input vector as in the first case. In the third case, the proposed neural networks are trained to predict only one component ( X n +1 , Y n +1 , or Z n +1 ) of the attractors, given a number of past values of the same component. Finally, the ability of the networks to predict the Y and Z components of an X time series of the dynamical systems is examined. Since the response of some networks is not satisfactory, the distribution of absolute error is considered in order to form a realistic picture of the networks' performance. [ABSTRACT FROM AUTHOR]