细胞神经网络的稳定性分析

【作者】 梁莉；

【导师】 钟守铭；

【作者基本信息】 电子科技大学 ， 应用数学， 2006， 硕士

【摘要】 针对稳定性理论在细胞神经网络中的巨大影响,本文主要探讨了时滞细胞神经网络系统、模糊细胞神经网络的全局渐近稳定性和全局指数稳定性以及随机细胞神经网络的均方指数稳定性和几乎必然指数稳定性。全文共分为五章。第一章是引言,概括了稳定性基本理论,引出研究细胞神经网络稳定性的意义,总结了该文主要涉及内容。在第二章里考虑的是时滞的细胞神经网络模型,在这里我们放弃了激励函数是可微的要求,只需要满足Lipschisz连续条件。利用Halanay不等式和一些基本不等式,通过构造Lyapunov函数(泛函),我们进一步研究时滞细胞神经网络的稳定性问题,得出网络平衡态的全局渐近稳定性和全局指数稳定性的若干一般性判断依据;并给出了一系列的充分准则。第三章则主要研究具有一般性的时滞的随机神经网络的均方指数稳定性和几乎必然指数稳定性,它的特殊情况就是随机细胞神经网络模型和随机时滞Hopfield型的神经网络模型。在这里我们利用了Lyapunov函数与鞅不等式,其条件分为时滞无关和时滞相关,改进了已有的一些文献结果。第四章主要研究的是利用常数变易法或建立相应的Lyapunov函数(泛函)方法,和Razumikhin的思想等,以此取得模糊细胞神经网络的一些全局渐近稳定和全局指数稳定的充分条件,对已有一些文献进行了改进或推广。第五章则针对全文内容进行总结,并进行展望性探讨。更多还原

【Abstract】 Since stability theory has enormous impact on cellular neural networks, in this paper, we mostly probe into the global asymptotic stability and global exponential stability for cellular neural networks with delays, as well as mean square exponential stability and almost surely exponential stability for stochastic cellular neural networks. The paper comprises five chapters.In Chapter 1, the preface generalizes the basic theory of stability, derives the meaning of investigating stability for cellular neural networks, and sums up the central content of the paper.In Chapter 2,we consider cellular neural networks with delays, where we discard the demand that the activation functions must be derivable and only request them to be Lipschitz continuous. Using Halanay inequality and the technique of some basal inequality analysis, along with constructing newer Lyapunov function(functional) than which has been adopted in some literature ever, we ulteriorly study the stability issue of cellular neural networks, and obtain some judging conditions, as well as present some series of sufficient rules.In Chapter 3, we mainly probe into mean square exponential stability and almost surely exponential stability for stochastic delayed neural networks. Its especial instances are stochastic cellular neural networks and stochastic delayed Hopfield neural networks. In the section, we utilize Lyapunov function and Young inequality, providing with delay independent conditions and delay dependent conditions, which improve the results of some literatures.In Chapter 4, we mainly investigate that applying the method of variation of the parameters、constructing corresponding Lyapunov function(functional)、using Razum- ikhin ideology and so on, we obtain some sufficient conditions on globally asymptotic stability and global exponential stability of fuzzy cellular neural networks. These improve or generalize the results about some literatures.In the last chapter, we summarize the content of the article, and go along expecting discussion.更多还原