The authors in their papers (Liao and Mao, Stochast. Anal. Appl. 14 (2) (1996a) 165–185; Neural, Parallel Sci. Comput. 4 (2) (1996b) 205–244) initiated the study of stability and instability of stochastic neural networks and this paper is the continuation of their research in this area. The main aim of this paper is to discuss almost sure exponential stability for a stochastic delay neural network d x(t)=[−Bx(t)+Ag(x τ (t))] d t+σ(x(t),g(x τ (t),t) d w(t) . The techniques used in this paper are different from those in their earlier papers. Especially, the nonnegative semimartingale convergence theorem will play an important role in this paper. Several examples are also given for illustration.

Stability of stochastic delay neural networks

This paper is concerned with the problem of exponential stability for a class of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays and known or unknown parameters. The jumping parameters are determined by a continuous-time, discrete-state Markov chain, and the mixed time delays under consideration comprise both time-varying delays and continuously distributed delays. To the best of the authors' knowledge, till now, the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper. The main objective of this paper is to fill this gap. By constructing a novel Lyapunov-Krasovskii functional, and using some new approaches and techniques, several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square. The results presented in this paper generalize and improve many known results. Finally, two numerical examples and their simulations are given to show the effectiveness of the theoretical results.

Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays

In this paper, the problem of exponential stability is investigated for a class of stochastic neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modeled as a continuous-time finite-state Markov chain. Based on a Lyapunov-Krasovskii functional and the stochastic analysis theory, a linear matrix inequality (LMI) approach is developed to derive some novel sufficient conditions, which guarantee the exponential stability of the equilibrium point in the mean square. The proposed LMI-based criteria are quite general since many factors, such as noise perturbations, Markovian jump parameters, and mixed time delays, are considered. In particular, the mixed time delays in this paper synchronously consist of constant, time-varying, and distributed delays, which are more general than those discussed in the previous literature. In the latter, either constant and distributed delays or time-varying and distributed delays are only included. Therefore, the results obtained in this paper generalize and improve those given in the previous literature. Two numerical examples are provided to show the effectiveness of the theoretical results and demonstrate that the stability criteria used in the earlier literature fail.

Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays

The ordinary Takagi-Sugeno (TS) fuzzy models have provided an approach to represent complex nonlinear systems to a set of linear sub-models by using fuzzy sets and fuzzy reasoning. In this paper, stochastic fuzzy Hopfield neural networks with time-varying delays (SFVDHNNs) are studied. The model of SFVDHNN is first established as a modified TS fuzzy model in which the consequent parts are composed of a set of stochastic Hopfield neural networks with time-varying delays. Secondly, the global exponential stability in the mean square for SFVDHNN is studied by using the Lyapunov-Krasovskii approach. Stability criterion is derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages.

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Stochastic stability analysis of fuzzy hopfield neural networks with time-varying delays

Mean square exponential stability of stochastic delayed Hopfield neural networks

In this paper we shall discuss stochastic effects to the stability property of a neural network Suppose the stochastically perturbed neural network is described by an Ito equation [ILM002]The Geral theory on the almost sure exponential stability and instability of the stochastically perturbed neural network is first established. The theory is then applied to investigate the stochastic stabilization and destabilization of the neural network. Several interesting examples are also given for illustration

X.X. Liao

Papers

Exponential stability and instability of stochastic neural networks 1