Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters

In this paper, the problem of stochastic stability for a class of time-delay Hopfield neural networks with Markovian jump parameters is investigated. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Without assuming the boundedness, monotonicity and differentiability of the activation functions, some results for delay-dependent stochastic stability criteria for the Markovian jumping Hopfield neural networks (MJDHNNs) with time-delay are developed. We establish that the sufficient conditions can be essentially solved in terms of linear matrix inequalities.     

Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays

This paper discusses a generalized model of high-order Hopfield-type neural networks with time-varying delays. Some novel global stability criteria of the system is derived by using Lyapunov method, linear matrix inequality (LMI) and analytic technique. The LMI-based criteria obtained here are computationally more flexible and more generic than many other existing criteria. A numerical example is given to illustrate our result.     

Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates

In this paper, the problem of stochastic stability criterion of Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates is considered. Some new delay-dependent stability criteria are derived by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks

This paper is concerned with the existence and exponential stability of positive almost periodic solutions of high-order Hopfield neural networks (HHNNs) with time-varying delays. Some sufficient conditions for the existence and exponential stability of positive almost periodic solutions are established.     

Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays

In this paper we study the stability for a class of stochastic bidirectional associative memory (BAM) neural networks with reaction-diffusion and mixed delays. The mixed delays considered in this paper are time-varying and distributed delays. Based on a new Lyapunov-Krasovskii functional and the Poincaré inequality as well as stochastic analysis theory, a set of novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution. The obtained results show that the reaction-diffusion term does contribute to the exponentially stabilization of the considered system. Moreover, two numerical examples are given to show the effectiveness of the theoretical results.     

Exponential stability for stochastic BAM networks with discrete and distributed delays

In this paper, we investigate exponential stability for stochastic BAM networks with mixed delays. The mixed delays include discrete and distributed time-delays. The purpose of this paper is to establish some criteria to ensure the delayed stochastic BAM neural networks are exponential stable in the mean square. A sufficient condition is established by consructing suitable Lyapunov functionals. The condition is expressed in terms of the feasibility to a couple LMIs. Therefore, the exponential stability of the stochastic BAM networks with discrete and distributed delays can be easily checked by using the numerically efficient Matlab LMI toobox. A simple example is given to demonstrate the usefulness of the derived LMI-based stability conditions.     

Exponential stability analysis for uncertain neural networks with interval time-varying delays

In this paper, the problem of exponential stability analysis for neural networks is investigated. It is assumed that the considered neural networks have norm-bounded parametric uncertainties and interval time-varying delays. By constructing a new Lyapunov functional, new delay-dependent exponential stability criteria with an exponential convergence rate are established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criteria.     

Global exponential stability of Hopfield neural networks with distributed delays

In this paper, dynamical behaviors of Hopfield neural networks system with distributed delays were studied. By using contraction mapping principle and differential inequality technique, a sufficient condition was obtained to ensure the existence uniqueness and global exponential stability of the equilibrium point for the model. Here we point out that our methods, which are different from previous known results, base on the contraction mapping principle and inequality technique. Two remarks were also worked out to demonstrate the advantage of our results.     

LMI-based criteria for stability of high-order neural networks with time-varying delay

This paper investigates the stability of a class of high-order neural networks with time-varying delay, which can be considered as an expansion of Hopfield neural networks and is seldom considered in the literature. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, sufficient conditions guaranteeing the global exponential stability of the equilibrium point are presented. Two examples are given to show the effectiveness of the proposed conditions. The obtained results are also shown to be different from and more general than existing ones.     

Robust stability for stochastic Hopfield neural networks with time delays

In this paper, the asymptotic stability analysis problem is considered for a class of uncertain stochastic neural networks with time delays and parameter uncertainties. The delays are time-invariant, and the uncertainties are norm-bounded that enter into all the network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov–Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be checked readily by using some standard numerical packages, and no tuning of parameters is required. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

Existence and stability of almost periodic solutions of Hopfield neural networks with continuously distributed delays

In this paper, the global stability and almost periodicity are investigated for Hopfield neural networks with continuously distributed neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and they complement the previously known ones. Finally, an example is given to demonstrate the effectiveness of our results.     

Exponential stability of Hopfield neural networks with time‐varying delays via impulsive control

In this paper, by utilizing the Lyapunov functionals, the analysis method and the impulsive control, we analyze the exponential stability of Hopfield neural networks with time‐varying delays. A new criterion on the exponential stabilization by impulses and the exponential stabilization by periodic impulses is gained. We can see that impulses do contribution to the system's exponential stability. Two examples are given to illustrate the effectiveness of our result. Copyright © 2010 John Wiley & Sons, Ltd.     

Global exponential stability of nonautonomous neural networks with time-varying delays and reaction-diffusion terms

A class of nonautonomous neural networks with time-varying delays and reaction-diffusion terms is considered. By means of Lyapunov functionals and differential inequality techniques, criteria on global exponential stability of this model with the Neumann boundary conditions and the Dirichlet boundary conditions are derived, respectively. The results of this paper are new and they improve and generalize previously known results.     

时滞Hopfield神经网络的全局指数稳定性

讨论带有可变时滞的Hopfield神经网络的全局指数稳定性.在非线性激励函数满足Lipschitz条件的假设下,利用推广的Halanay不等式,Dini导数和分析技巧,建立了这类神经网络系统全局指数稳定的几个判别准则.这些判别准则仅仅依赖于系统的参数.     

On exponential stability analysis for neural networks with time-varying delays and general activation functions

This paper is concerned with the exponential stability analysis for a class of cellular neural networks with both interval time-varying delays and general activation functions. The boundedness assumption of the activation function is not required. The limitation on the derivative of time delay being less than one is relaxed and the lower bound of time-varying delay is not restricted to be zero. A new Lyapunov-Krasovskii functional involving more information on the state variables is established to derive a novel exponential stability criterion. The obtained condition shows potential advantages over the existing ones since no useful item is ignored throughout the estimate of upper bound of the derivative of Lyapunov functional. Finally, three numerical examples are included to illustrate the proposed design procedures and applications.     

Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays

In this paper, by means of constructing the extended impulsive delayed Halanay inequality and by Lyapunov functional methods, we analyze the global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. Some new sufficient conditions ensuring exponential stability of the unique equilibrium point of impulsive Hopfield neural networks with time delays are obtained. Those conditions are more feasible than that given in the earlier references to some extent. Some numerical examples are also discussed in this work to illustrate the advantage of the results we obtained.     

Stationary oscillation for high-order Hopfield neural networks with time delays and impulses

We investigate stationary oscillation for high-order Hopfield neural networks with time delays and impulses. In a recent paper [J. Zhang, Z. J. Gui, Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays, Journal of Computational and Applied Mathematics 224 (2008) 602-613], the authors claim that they obtain a criterion of existence, uniqueness, and global exponential stability of periodic solution (i.e. stationary oscillation) for high-order Hopfield neural networks with time delays and impulses. In this paper, we point out that the main result of the recent paper is unture, and present a new sufficient condition of stationary oscillation for the neural networks. A numerical example is given to illustrate the effectiveness of the obtained result.     

Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses

In this paper we investigate a class of Hopfield neural networks subject to periodic impulses. First we give sufficient conditions to ensure existence and exponential stability of the anti-periodic solutions, which are new and complementary to previously known results. Then we present an example to demonstrate our results.     

Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, the global exponential stability and periodicity are investigated for a class of delayed high-order Hopfield neural networks (HHNNs) with impulses, which are new and complement previously known results. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results. The numerical simulation shows that our models can occur in many forms of complexities including periodic oscillation and the Gui chaotic strange attractor.