Huan Su

Global stability analysis for stochastic coupled systems on networks

This paper considers the global stability problem for some stochastic coupled systems on networks (SCSNs). We provide a systematic method for constructing a global Lyapunov function for these SCSNs, by using graph theory and the Lyapunov second method. Consequently, a new global stability principle, which has a close relation to the topology property of the network, is given. As an application to the results, we employ the principle to two well-known coupled systems in physical and ecology, and then some easy-verified sufficient conditions which guarantee the global stability are obtained.

Global stability for discrete Cohen–Grossberg neural networks with finite and infinite delays

Abstract In this paper, the global stability problem for a general discrete Cohen–Grossberg neural network with finite and infinite delays is investigated. A simple criterion ensuring the global asymptotical stability is established, by applying the Lyapunov method and graph theory. Finally, an example showing the effectiveness of the provided criterion is given.

A graph-theoretic approach to boundedness of stochastic Cohen-Grossberg neural networks with Markovian switching

In this paper, a novel class of stochastic Cohen-Grossberg neural networks with Markovian switching (SCGNNMSs) is investigated, where the white noise and the color noise are taken into account. By utilizing Lyapunov method, some graph theory and M-matrix technique, several sufficient conditions are obtained to ensure the asymptotic boundedness of the SCGNNMSs. These criteria have a close relation to the topology property of the network and are easy to be verified in practice. Two numerical examples are also presented to substantiate the theoretical results.

Synchronization in time-discrete delayed chaotic systems

This paper uses the Euler method to a delayed chaotic system, resulting that a time-discrete drive system is obtained. And then a time-discrete response system with negative feedback and impulsive effect is designed. Some sufficient conditions are given to ensure that the drive-response systems are globally impulsively exponentially synchronized. At last, the effective and the feasibility of the drive-response systems are illustrated by some numerical examples.

Asymptotic boundedness for stochastic coupled systems on networks with Markovian switching

Abstract In this paper, a novel class of stochastic coupled systems on networks with Markovian switching is presented. In such model, the white noise, the color noise and the coupling between different vertices of the network are taken into account. Focusing on the boundedness problem, this paper employs the Lyapunov method, some graph theory and the method of M -matrix to establish some simple and easy-verified boundedness criteria. These criteria can directly show the link between the graph structure of the network and the dynamics of coupled systems. Finally, stochastic coupled van der Pol׳s equations with Markovian switching are used to demonstrate our findings. Meanwhile, two numerical examples are also provided to clearly show the influence of coupled structure on the boundedness of coupled systems.

Stability analysis for stochastic neural network with infinite delay

This paper considers a stochastic neural network (SNN) with infinite delay. Some sufficient conditions for stochastic stability, stochastic asymptotical stability and global stochastic asymptotical stability, respectively, are derived by means of Lyapunov method, Ito formula and some inequalities. As a corollary, we show that if the neural network with infinite delay is stable under some conditions, then the stochastic stability is maintained provided the environmental noises are small. Estimates on the allowable sizes of environmental noises are also given. Finally, a three-dimensional SNN with infinite delay is analyzed and some numerical simulations are illustrated to show our results.

Global stochastic stability analysis for stochastic neural networks with infinite delay and Markovian switching

We consider a novel stochastic NNs model.The method is the Lyapunov method, stochastic analysis technique and M-matrix theory.We derive sufficient criteria for three kinds of stochastic stability.Numerical examples demonstrate the applicability and effectiveness of the theoretical theorems. This paper focuses on the stochastic stability for a novel kind of stochastic neural networks with infinite delay and Markovian switching. By using the Lyapunov method, stochastic analysis technique and M-matrix theory, some simple and easily testable sufficient conditions are presented to ensure the trivial solution is stochastically stable, stochastically asymptotically stable, and globally stochastically asymptotically stable, respectively. As a subsequent result, we develop the conditions that guarantee global stochastic asymptotic stability for stochastic neural networks with infinite delay, as well as global asymptotic stability for neural networks with infinite delay. From the perspective of theory, the derived stability criteria include some existing ones as its special cases, and are thus less conservative. Finally, two examples are given to demonstrate the applicability and effectiveness of the theoretical theorems.

The existence and exponential stability of periodic solution for coupled systems on networks without strong connectedness

Abstract This paper focuses on the problem of the existence and global exponential stability of periodic solution for coupled systems with delays on networks without strong connectedness (NWSC), which extends previous results of strongly connected networks. An innovative hierarchical method is proposed to characterize a large NWSC. Then each layer consists of several independent strongly connected subnets. By using the existing results of strongly connected networks and constructing auxiliary systems, we investigate the existence of periodic solution for original coupled systems on NWSC layer by layer. Moreover, the uniqueness and global exponential stability of periodic solution are considered as well. Then the theoretical results are applied to coupled oscillators on NWSC. Finally, a numerical example is also provided to illustrate the effectiveness of the theoretical results.