Chuangxia Huang

Almost sure exponential stability of stochastic cellular neural networks with unbounded distributed delays

In this paper, a cellular neural network whose state variables are governed by stochastic non-linear integro-differential equations is investigated. The considered delays are distributed continuously over unbounded intervals. By applying the Lyapunov functional method, the semimartingale convergence theorem, and some inequality technique, we obtain some sufficient criteria to check the almost sure exponential stability of the system, which generalizes and improves some earlier publications. Two examples are also given to demonstrate our results.

On pth moment exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays

With the help of Lyapunov function, stochastic analysis technique, generalized Halanay inequality and Hardy inequality, a set of novel sufficient conditions on pth moment exponential stability for non-autonomous stochastic Cohen-Grossberg neural networks is given, which modifies and generalizes some corresponding published results.

Convergence Dynamics of Stochastic Cohen–Grossberg Neural Networks With Unbounded Distributed Delays

This paper addresses the issue of the convergence dynamics of stochastic Cohen-Grossberg neural networks (SCGNNs) with white noise, whose state variables are described by stochastic nonlinear integro-differential equations. With the help of Lyapunov functional, semi-martingale theory, and inequality techniques, some novel sufficient conditions on pth moment exponential stability and almost sure exponential stability for SCGNN are given. Furthermore, as byproducts of our main results, some sufficient conditions for checking stability of deterministic CGNNs with unbounded distributed delays have been established. Especially, even when the spectral radius of the coefficient matrix is greater than 1, in some cases our theory is also effective.

Global stability analysis of a class of delayed cellular neural networks

Employing Brouwers fixed point theorem, matrix theory, a continuation theorem of the coincidence degree and inequality analysis, the authors study further global exponential stability and the existence of periodic solutions of a class of cellular neural networks with delays (DCNNs) in this paper. A family of sufficient conditions is given for checking global exponential stability and the existence of periodic solutions of DCNNs. The results extend and improve the earlier publications.

Almost sure exponential stability of delayed Hopfield neural networks

The stability of stochastic delayed Hopfield neural networks (DHNN) is investigated in this paper. Under the help of suitable Lyapunov function and the semimartingale convergence theorem, we obtain some sufficient criteria to check the almost sure exponential stability of the DHNN.

Lag stochastic synchronization of chaotic mixed time-delayed neural networks with uncertain parameters or perturbations

This paper investigates the problem of lag synchronization for a kind of chaotic neural networks with discrete and distributed delays (mixed delays). The driver system has uncertain parameters and uncertain nonlinear external perturbations, while the response system has channel noises. A simple but all-powerful robust adaptive controller is designed to circumvent the effects of uncertain external perturbations such that the response system synchronize with the driver system. Based on the invariance principle of stochastic differential equations and some suitable Lyapunov functions, several sufficient conditions are developed to solve this problem. Moreover, under certain conditions, parameters of the uncertain master system can be estimated. Numerical simulations are exploited to show the effectiveness of the theoretical results.

Existence and global exponential stability of periodic solution of two-neuron networks with time-varying delays

Abstract This paper is concerned with a delay differential system { x ( t ) = − a 1 ( t ) x ( t ) + b 1 ( t ) f 1 ( x ( t − τ 1 ( t ) ) , y ( t − τ 2 ( t ) ) ) + I 1 ( t ) , y ( t ) = − a 2 ( t ) y ( t ) + b 2 ( t ) f 2 ( x ( t − τ 3 ( t ) ) , y ( t − τ 4 ( t ) ) ) + I 2 ( t ) . Such a differential system can be regarded as a model of a two-neuron artificial neural network with delayed feedback. Some interesting results are obtained for the existence and exponential stability of the periodic solution for the system. Our approach is based on the continuation theorem of the coincidence degree, a priori estimates, and differential inequalities.

An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays

This paper investigates the problem of exponential synchronization of switched stochastic competitive neural networks (SSCNNs) with both interval time-varying delays and distributed delays. The distributed delays can be unbounded or bounded; the stochastic perturbation is of the form of multi-dimensional Brownian motion, and the networks are governed by switching signals with average dwell time. Based on new multiple Lyapunov-Krasovkii functionals, the free-weighting matrix method, Newton-Leibniz formulation, as well as the invariance principle of stochastic differential equations, two sufficient conditions ensuring the exponential synchronization of drive-response SSCNNs are developed. The provided conditions are expressed in terms of linear matrix inequalities, which are dependent on not only both lower and upper bounds of the interval time-varying delays but also delay kernel of unbounded distributed delays or upper bounds for bounded distributed delays. Control gains and average dwell time restricted by given conditions are designed such that they are applicable in practice. Numerical simulations are given to show the effectiveness of the theoretical results.

Dynamic Analysis of Stochastic Recurrent Neural Networks

This paper addresses the issue of pth moment exponential stability of stochastic recurrent neural networks (SRNN) with time-varying interconnections and delays. With the help of the Dini derivative of the expectation of V(t, X(t)) “along” the solution X(t) of the model and the technique of Halanay-type inequality, some novel sufficient conditions on pth moment exponential stability of the trivial solution has been established. Conclusions of the development as presented in this paper have gone beyond some published results and are helpful to design stability of networks when stochastic noise is taken into consideration. An example is also given to illustrate the effectiveness of our results.

Stochastic Synchronization of Reaction-Diffusion Neural Networks under General Impulsive Controller with Mixed Delays

This paper investigates drive-response synchronization of a class of reaction-diffusion neural networks with time-varying discrete and distributed delays via general impulsive control method. Stochastic perturbations in the response system are also considered. The impulsive controller is assumed to be nonlinear and has multiple time-varying discrete and distributed delays. Compared with existing nondelayed impulsive controller, this general impulsive controller is more practical and essentially important since time delays are unavoidable in practical operation. Based on a novel impulsive differential inequality, the properties of random variables and Lyapunov functional method, sufficient conditions guaranteeing the global exponential synchronization in mean square are derived through strict mathematical proof. In our synchronization criteria, the distributed delays in both continuous equation and impulsive controller play important role. Finally, numerical simulations are given to show the effectiveness of the theoretical results.