Cohen-Grossberg神经网络的全局指数稳定性分析

本文研究了CohenGrossberg神经网络模型的指数稳定性.为避免构造Lyapunov函数的困难,我们采用广义相对Dalquist数方法来分析神经网络的稳定性.借助这一方法,我们不但得到了CohenGrossberg神经网络模型平衡解的存在性、唯一性和全局指数稳定性的新的充分条件,而且给出了神经网络的指数衰减估计.所获结论改进了已有文献的相关结果.     

具有时滞的一般型脉冲神经网络的指数稳定性

讨论具有时滞的一般性脉冲神经网络的稳定性.在不假定激励函数有界或可导的前提下,利用非光滑分析和Lyapunov泛函,得到了这类神经网络系统平衡点的存在唯一性和全局指数稳定性判别准则.作为特例,得到了Hopfield神经网络,时滞细胞神经网络,双向联想记忆神经网络的平衡点的存在唯一性和全局指数稳定性判定定理.     

反应扩散递归神经网络全局指数稳定的鲁棒分析

主要讨论反应扩散递归神经阿络全局指数稳定的鲁棒分析.给定反应扩散递归神经网络是全局指数稳定,首先,在此神经网络基础上考虑噪音扰动,利用超越方程得到噪音密度的上界,在上界范围内,带噪音的反应扩散递归神经网络仍然是全局指数稳定.进一步,在反应扩散递归神经网络基础上同时考虑噪音扰动和连接权参数不确定,利用超越方程得到连接权参数和噪音密度上界,在两个参数描述的超越方程范围内,带噪音和连接权参数不确定的反应扩散递归神经网络仍然是全局指数稳定.最后给出数值算例证实相关理论的有效性.     

随机变时滞模糊神经网络的均方指数稳定性

利用Lyapunov泛函和随机分析的方法,研究了一类具有变时滞随机模糊细胞神经网络的均方指数稳定性,得到了这类神经网络均方指数稳定性的充分条件.数值例子说明了得到的结果的有效性.     

Cohen-Grossberg神经网络指数稳定性的新判则

避免构造Lyapunov函数的困难,运用广义Dahlquist数方法研究了Cohen- Grossberg神经网络模型的指数稳定性,不但得到了Cohen-Grossberg神经网络平衡点存在惟一性和指数稳定性的全新充分条件,而且给出了神经网络的指数衰减估计.与已有文献结果相比,所得的神经网络指数稳定的充分条件更为宽松,给出的解的指数衰减速度估计也更为精确.     

时滞BAM神经网络周期解的存在性和全局指数稳定性

本文利用迭合度理论,通过构造适当的Lyapunov泛函并结合Yang不等式分析技巧,获得了具周期系数的时滞BAM神经网络周期解的存在性和全局指数稳定性的充分条件,这些结果对设计全局指数稳定的BAM神经网络与周期振荡的BAM神经网络具有重要的指导意义.     

随机时滞神经网络系统指数稳定性的新判定准则(英文)

本文主要研究了一类随机时滞神经网络的稳定性条件.利用随机分析技巧和不动点原理,建立了一个关于随机时滞神经网络指数稳定性判定的新的准则.     

具有时滞的细胞神经网络的全局指数稳定性

利用Liapunov函数方法,结合积分不等式技巧,分析了时滞细胞神经网络的平衡点存在的唯一性和全局指数稳定性,保证时滞细胞神经网络全局指数稳定的一个新的充分判据被得到.所得判据比已有文献具有更少的限制,为实际应用提供了方便.     

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.     

一类变系数混合时滞神经网络周期解的存在性和指数稳定性

在不需要激活函数有界的条件下,利用分析技巧和Poincaré映射给出了一类变系数混合时滞神经网络周期解的存在、唯一和指数稳定的充分条件.结论对神经网络的设计具有重要的意义.     

Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays

This paper is concerned with interval general bidirectional associative memory (BAM) neural networks with proportional delays. Using appropriate nonlinear variable transformations, the interval general BAM neural networks with proportional delays can be equivalently transformed into the interval general BAM neural networks with constant delays. The sufficient condition for the existence and uniqueness of equilibrium point of the model is established by applying Brouwer's fixed point theorem. By constructing suitable delay differential inequalities, some sufficient conditions for the global exponential stability of the model are obtained. Two examples are given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. Copyright © 2016 John Wiley & Sons, Ltd.     

Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays

In this paper, we formulate and investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, the viability and dissipativity of solutions for functional differential inclusions and memristive BAM neural networks can be guaranteed by the matrix measure approach and generalized Halanay inequalities. Then, a new method involving the application of set-valued version of Krasnoselskii’ fixed point theorem in a cone is successfully employed to derive the existence of the positive periodic solution. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. The obtained results extend and improve some previous works on conventional BAM neural networks. Finally, numerical examples are given to demonstrate the theoretical results via computer simulations.     

New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays

In this paper, we consider the problem of passivity analysis issue for a class of stochastic fuzzy BAM neural networks with time varying delays. By employing the idea of delay-fractioning technique and Lyapunov stability theory, a new set of sufficient conditions are derived in terms of linear matrix inequalities for obtaining the passivity condition of the considered neural network model. First, we derive the passivity condition for stochastic fuzzy BAM neural networks with time varying delays and then the result is extended to the case with uncertainties. Two numerical examples are given to illustrate the effectiveness and conservatism of the obtained results.     

A new criterion to global exponential periodicity for discrete-time BAM neural network with infinite delays

The discrete-time bidirectional associative memory neural network with periodic coefficients and infinite delays is studied. And not by employing the continuation theorem of coincidence degree theory as other literatures, but by constructing suitable Liapunov function, using fixed point theorem and some analysis techniques, a sufficient criterion is obtained which ensures the existence and global exponential stability of periodic solution for the type of discrete-time BAM neural network. The obtained result is less restrictive to the BAM neural networks than previously known criteria. Furthermore, it can be applied to the BAM neural network which signal transfer functions are neither bounded nor differentiable. In addition, an example and its numerical simulation are given to illustrate the effectiveness of the obtained result.     

NEW CRITERIA OF EXPONENTIAL STABILITY FOR BAM NEURAL NETWORKS WITH DELAYS

In this Letter,a novel Lyapunov functional is constructed to investigate the exponential stability of the BAM neural networks.New sufficient conditions of the uniqueness and global exponential stability for the equilibrium of BAM neural networks with delays are obtained.The results improve those existing ones.     

Fixed-time synchronization of a reaction-diffusion BAM neural network with distributed delay and its application to image encryption

In this paper, the fixed-time synchronization of reaction-diffusion BAM neural networks is investigated, where both discrete and distributed delays are taken into account. Combining Lyapunov stability theory and several integral inequalities, fixed-time synchronization criteria are established. Through sensitivity analysis, we find the key controller parameters that have a great influence on the maximum settling time. Using the chaotic sequences generated by the neural network, the color image can be encrypted by the Arnold Cat Map and the pixel diffusion. Experiments show that the image encryption algorithm designed in this paper has good properties of security and anti-attacking, which meets the requirements for the secure transmission of image information.     

Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses

In this paper, we present a general class of BAM neural networks with discontinuous neuron activations and impulses. By using the fixed point theorem in differential inclusions theory, we investigate the existence of periodic solution for this neural network. By constructing the suitable Lyapunov function, we give a sufficient condition which ensures the uniqueness and global exponential stability of the periodic solution. The results of this paper show that the Forti’s conjecture is true for BAM neural networks with discontinuous neuron activations and impulses. Further, a numerical example is given to demonstrate the effectiveness of the results obtained in this paper.     

A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays

This paper presents an easily verifiable delay independent sufficient condition for the global robust asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with time delays by employing a class of Lyapunov functionals. The obtained results are applicable to all bounded continuous non-monotonic neuron activation functions. Some numerical examples are given to compare our results with the previous robust stability results derived in the literature.