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.     

Global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms

In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction–diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits.     

Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays

The authors discuss the existence of the equilibrium point and its global exponential stability of reaction-diffusion cellular neural networks (RDCNNs) with S-type distributed signal transmission delays along the axon of a neuron by means of the topological degree theory and differential inequality technique. A theorem and two corollaries were obtained in which the boundedness, monotonicity and differentiability conditions on the activation functions are not required. The sufficient conditions on global exponential stability established in this paper, which are easily verifiable, have a wider adaptive range.     

具有时滞的扩散BAM神经网络的指数稳定性

研究一类具有反应扩散的滞后BAM神经网络平衡点的存在性唯一性和全局指数稳定性.运用拓扑同胚映射,Lyapunov泛函以及多参数方法,得到关于平衡点存在唯一性和全局指数稳定性的充分条件,将相关文献的结果推广到正整数r范数上.     

Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.     

Global exponential stability of fuzzy BAM neural networks with transmission delays

In this paper, a class of fuzzy bidirectional associated memory (BAM) neural networks with transmission delays are studied. Some sufficient conditions are established for the existence , uniqueness and global exponential stability of equilibrium point. The sufficient conditions are easy to verify at pattern recognition and automatic control. Finally, an example is given to show feasibility and effectiveness of our results.     

Global exponential stability analysis on impulsive BAM neural networks with distributed delays

Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.     

Global exponential synchronization of delayed fuzzy cellular neural networks with impulsive effects

In this paper, synchronization of delayed fuzzy cellular neural networks has been considered. By construction a suitable Lyapunov functional and utilizing some inequality techniques, some sufficient conditions for synchronization of such a system are obtained. Simulation results are given to justify the theoretical analysis in this paper.     

Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays

In this paper, the global exponential stability for neutral-type impulsive neural networks with discrete and distributed delays is established by utilizing the Lyapunov–Krasovskii functional combining with the linear matrix inequality(LMI) approach.     

Global exponential stability for nonautonomous cellular neural networks with unbounded delays

Global exponential stability of nonautonomous cellular neural networks with unbounded delays is considered in this paper. By applying Lyapunov functional method, some new sufficient conditions are given for global exponential stability of solutions of the networks. The stability conditions obtained here improve and extend some of the previous conditions. An example is presented to illustrate the applicability of these conditions.     

Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction-diffusion terms

This paper is concerned with global asymptotic stability of a class of reaction-diffusion stochastic Bi-directional Associative Memory (BAM) neural networks with discrete and distributed delays. Based on suitable assumptions, we apply the linear matrix inequality (LMI) method to propose some new sufficient stability conditions for reaction-diffusion stochastic BAM neural networks with discrete and distributed delays. The obtained results are easy to check and improve upon the existing stability results. An example is also given to demonstrate the effectiveness of the obtained results.     

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.     

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.     

Global asymptotic stability of stochastic reaction-diffusion neural networks with time delays in the leakage terms

In this paper, a class of stochastic reaction-diffusion neural networks with time delays in the leakage terms is investigated. By using the Lyapunov functional method and linear matrix inequality (LMI) approach, sufficient conditions are derived to ensure the global asymptotic stability of an equilibrium point of the networks in the mean square. The results can be easily solved by MATLAB LMI toolbox. Finally, a numerical example is given to demonstrate the effectiveness and conservativeness of our theoretical results.     

Global exponential stability for BAM neural networks with time-varying delays in the leakage terms

In this paper, we first investigate the existence of a unique equilibrium to general bidirectional associative memory neural networks with time-varying delays in the leakage terms by the fixed point theorem. Then, by constructing a Lyapunov functional, we establish some sufficient conditions on the global exponential stability of the equilibrium for such neural networks, which substantially extend and improve the main results of Gopalsamy [K. Gopalsamy, Leakage delays in BAM, J. Math. Anal. Appl. 325 (2007) 1117–1132].     

Delay-dependent exponential stability of cellular neural networks with time-varying delays

The global exponential stability of cellular neural networks (CNNs) with time-varying delays is analyzed. Two new sufficient conditions ensuring global exponential stability for delayed CNNs are obtained. The conditions presented here are related to the size of delay. The stability results improve the earlier publications. Two examples are given to demonstrate the effectiveness of the obtained results.     

Global exponential stability of interval neural networks with variable delays

In this work, the conditions ensuring existence, uniqueness, and global exponential stability of the equilibrium point of interval neural networks with variable delays are studied. Applying the idea of the vector Lyapunov function, and M-matrix theory, the sufficient conditions for global exponential stability of interval neural networks are obtained.     

Global exponential stability of Cohen-Grossberg neural networks with variable delays

A class of generalized Cohen-Grossberg neural networks（CGNNs） with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.     

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.