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.     

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.     

Exponential stability of positive neural networks in bidirectional associative memory model with delays

This paper is concerned with the problem of exponential stability of positive neural networks in bidirectional associative memory (BAM) model with multiple time‐varying delays and nonlinear self‐excitation rates. On the basis of a systematic approach involving extended comparison techniques via differential inequalities, we first prove the positivity of state trajectories initializing from a positive cone called the admissible set of initial conditions. In combination with the use of Brouwer's fixed point theorem and M‐matrix theory, we then derive conditions for the existence and global exponential stability of a unique positive equilibrium of the model. An extension to the case of BAM neural networks with proportional delays is also presented. The effectiveness of the obtained results is illustrated by a numerical example with simulations.     

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.     

A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion

This paper deals with the problem of global exponential stability for bidirectional associate memory (BAM) neural networks with time-varying delays and reaction-diffusion terms. By using some inequality techniques, graph theory as well as Lyapunov stability theory, a systematic method of constructing a global Lyapunov function for BAM neural networks with time-varying delays and reaction-diffusion terms is provided. Furthermore, two different kinds of sufficient principles are derived to guarantee the exponential stability of BAM neural networks. Finally, a numerical example is carried out to demonstrate the effectiveness and applicability of the theoretical results.     

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.     

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.     

Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays

In this paper, based on the topological degree theory, Lyapunov functional method and inequality analysis technique, the existence and global exponential stability of equilibrium of impulsive fuzzy Cohen–Grossberg bi‐directional associative memory neural networks with delays, are investigated. Moreover, an illustrative example is given to demonstrate the effectiveness of the results obtained. Copyright © 2012 John Wiley & Sons, Ltd.     

Periodic bidirectional associative memory neural networks with distributed delays

Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin's coincidence degree theory and the Lyapunov functional method and the Young's inequality technique. These results are helpful for designing a globally exponentially stable and periodic oscillatory BAM neural network, and the conditions can be easily verified and be applied in practice. An example is also given to illustrate our results.     

Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays

This paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable Lyapunov function and a new differential inequality. The proposed method can also be applied to study the impulsive Cohen-Grossberg-type BAM neural networks with finite distributed delays. The results in this paper extend and improve the earlier publications. Finally, two examples with numerical simulations are given to demonstrate the obtained results.     

Existence and exponential stability of almost periodic solutions for neutral‐type BAM neural networks with distributed leakage delays

This paper is concerned with a class of neutral‐type BAM neural networks with distributed leakage delays. By applying the exponential dichotomy of linear differential equations, Lyapunov functional method and contraction mapping principle, we establish some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such BAM neural networks. An example is given to illustrate the effectiveness of the theoretical findings. The results obtained in this article are completely new and complement the previously known studies. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence and global exponential stability of almost periodic solutions for BAM neural networks with distributed leakage delays on time scales

In this paper, we deal with a class of BAM neural networks with distributed leakage delays on time scales. Some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such class of BAM neural networks are obtained by applying the exponential dichotomy of linear differential equations, Lapunov functional method and contraction mapping principle. An example is given to illustrate the effectiveness of the theoretical predictions. The obtained results in this paper are completely new and complement the previously known publications.     

Global exponential stability of a class of neural networks with delays

This paper is concerned with the stability of neural networks with time-varying delays. Under assumption that the nonlinear stimulate functions are Lipschitz continuous, by means of generalized Halanay inequalities, Dini＇s derivative and functional analysis techniques, several globally exponential stability criteria are established, which are only dependent on the parameters of the system.     

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.     

一类具有Leakage时滞的惯性Cohen-Grossberg神经网络的全局指数稳定性和Hopf分支

研究一类具有Leakage时滞的惯性Cohen-Grossberg神经网络模型.通过构造适当的Lyapunov泛函得到了平衡点全局指数稳定的充分条件.通过分析特征方程,讨论了系统平衡点的局部稳定性,得出了系统Hopf分支存在的充分条件.最后对所得理论结果进行了数值模拟.     

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 for a class of generalized delayed neural networks with impulses

In this paper, by utilizing Lyapunov functional method, the quality of negative definite matrix and the linear matrix inequality approach, the global exponential stability of the equilibrium point for a class of generalized delayed neural networks with impulses is investigated. A new criterion on global exponential stability is obtained. The result is related to the size of delays and impulses. An example is given to illustrate the effectiveness of our result. Copyright © 2011 John Wiley & Sons, Ltd.     

变时滞BAM神经网络的全局指数稳定性

研究一类变时滞BAM神经网络平衡点的全局指数稳定性问题.在不要求激励函数全局Lipschitz条件下,通过构造合适的Lyapunov泛函,并结合Young不等式,得到了BAM神经网络模型在一定条件下全局指数稳定的一些充分条件,推广和改进了前人的相关结论,为综合设计指数稳定的时滞BAM神经网络提供了依据.     

Global exponential stability analysis of bidirectional associative memory neural networks with time-varying delays

In this paper, global exponential stability is studied for a class of high-order bidirectional associative memory (BAM) neural networks with time-varying delays. An approach combining the Lyapunov functional with the Linear Matrix Inequality (LMI) is taken to study the problems. Several sufficient conditions are presented for ensuring the system to be globally exponentially stable. Three typical examples are presented to show the application of the criteria obtained in this paper.