Search

In this study, the authors study the finite‐time cluster synchronisation problem for a class of Markovian switching complex networks with stochastic noise perturbations. By constructing the suitable stochastic Lyapunov–Krasovskii functional, using finite‐time stability theorem, inequality techniques and the properties of Weiner process, sufficient conditions are obtained to ensure finite‐time cluster synchronisation for the complex networks with or without time delays. The effects of control parameters on cluster synchronisation speed and time delays are also analysed. Since finite‐time cluster synchronisation means the optimality in convergence time and has better robustness and disturbance rejection properties, this study has important theory significance and practical application value. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the exponential synchronization problem of Markovian jump genetic oscillators with partly unknown transition probabilities. We consider three types of feedback delays: feedback with nonidentical delay, feedback without self delay and feedback with identical delay. Based on Lyapunov functional methods and stochastic analysis techniques, the synchronization problem of genetic oscillators are derived. Finally, an example is given to illustrate the effectiveness of the derived results. [Copyright &y& Elsevier]

Abstract: In this paper, the stability analysis problem is investigated for a class of Markovian jumping genetic regulatory networks (GRNs) with mixed time delays (discrete time delays and distributed time delays) and stochastic perturbations. The main purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid and protein is asymptotically stable. By utilizing a more general Lyapunov–Krasovskii functional based on the idea of “delay decomposing” and the LMI (linear matrix inequality) technique, we derive sufficient delay-dependent conditions ensuring the asymptotically stability of the GRNs with mixed time delays and noise perturbations in terms of LMI. Finally, simulation examples are exploited to illustrate the effectiveness of the developed theoretical results. [Copyright &y& Elsevier]

In this letter, a general model of an array of N linearly coupled chaotic neural networks with hybrid coupling is proposed, which is composed of constant coupling, time-varying delay coupling and distributed delay coupling. The complex network jumps from one mode to another according to a Markovian chain with known transition probability. Both the coupling time-varying delays and the coupling distributed delays terms are mode-dependent. By the adaptive feedback technique, several sufficient criteria have been proposed to ensure the synchronization in an array of jump chaotic neural networks with mode-dependent hybrid coupling and mixed delays in mean square. Finally, numerical simulations illustrated by mode switching between two complex networks of different structure dependent on mode switching verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the problem of exponential synchronization for stochastic jumping chaotic neural networks (SJCNNs) with mixed delays and sector non-linearities. Based on Lyapunov–Krasovskii functional and free-weighting matrix method, a delay-dependent feedback controller with sector non-linearities is proposed to achieve the synchronization in mean square in terms of linear matrix inequalities (LMIs). The activation functions are assumed to be of more general descriptions. Finally, the corresponding simulation results show the effectiveness of the proposed criteria. [Copyright &y& Elsevier]

Abstract: This paper presents a novel particle swarm optimization (PSO) algorithm based on Markov chains and competitive penalized method. Such an algorithm is developed to solve global optimization problems with applications in identifying unknown parameters of a class of genetic regulatory networks (GRNs). By using an evolutionary factor, a new switching PSO (SPSO) algorithm is first proposed and analyzed, where the velocity updating equation jumps from one mode to another according to a Markov chain, and acceleration coefficients are dependent on mode switching. Furthermore, a leader competitive penalized multi-learning approach (LCPMLA) is introduced to improve the global search ability and refine the convergent solutions. The LCPMLA can automatically choose search strategy using a learning and penalizing mechanism. The presented SPSO algorithm is compared with some well-known PSO algorithms in the experiments. It is shown that the SPSO algorithm has faster local convergence speed, higher accuracy and algorithm reliability, resulting in better balance between the global and local searching of the algorithm, and thus generating good performance. Finally, we utilize the presented SPSO algorithm to identify not only the unknown parameters but also the coupling topology and time-delay of a class of GRNs. [ABSTRACT FROM AUTHOR]

A strongly ergodic non-homogeneous Markov chain is considered in the paper. As an analog of the Poisson limit theorem for a homogeneous Markov chain recurring to small cylindrical sets, a Poisson limit theorem is given for the non-homogeneous Markov chain. Meanwhile, some interesting results about approximation independence and probabilities of small cylindrical sets are given. [Copyright &y& Elsevier]

In this brief, the problem of almost surely exponential stability analysis is considered for neural networks with Lévy noise and Markovian switching. The switching parameters are generated from a continuous-time irreducible Markov chain taking value in a finite-state space. The purpose of the problem addressed is to derive a sufficient condition such that the dynamics of the neural network is almost surely exponentially stable. By generalized Itô׳s formula, strong law of large numbers for martingales and ergodicity of Markov chain, the stochastic analysis approach is developed to establish the desired condition which depends only on the stationary distribution of the Markov chain and some constants. Two numerical examples are given to verify the usefulness of the stability condition. [ABSTRACT FROM AUTHOR]