【作者】 潘瑞平；

【导师】 闫卫平；

【作者基本信息】 山西大学 ， 基础数学， 2009， 硕士

【摘要】 随着现代社会的发展,神经网络广泛的运用在工程,航空,经济,金融等方面.大多数情况下,时滞神经网络比神经网络能更好的解决问题.学者们已经取得了很大的成就,尤其是时滞神经网络平衡点和周期解的稳定性得到了深入的研究,也出现了一系列较好的结果.本文对几类具有时滞的神经网络模型进行了定性研究,讨论了这些神经网络平衡点的存在性,唯一性和全局指数稳定性及周期解的存在性和全局指数稳定性.全文的内容共分为四章:在第一章中,本文在[5]的基础上放宽了对激活函数有界的要求,研究了模型运用了压缩影像原理证平衡点的存在唯一性,并且构造李雅普诺夫函数法证的平衡点指数稳定的两个充分条件.进一步构造庞加莱映射研究了模型存在周期解且该周期解全局指数稳定.在第二章中,研究了一类具有脉冲的时滞泛函微分方程(可以推广到脉冲细胞神经网络和脉冲BAM自动联想神经网络中去)的周期解的全局指数稳定性.模型如下:利用线性矩阵不等式,采用矩阵谱半径性质和M矩阵法证的其周期解全局指数稳定性.并且进一步运用偏微分知识研究带扩散项的模型构造李雅普诺夫函数证明平衡点存在唯一且指数稳定性.并进一步研究模型在第三章中,本文在[19]的基础上,通过使用Halanay不等式,数学归纳法和不动点定理,研究了有脉冲的高阶细胞神经网络的周期解的指数稳定性.模型如下:在第四章中,本文在[31]的基础上,改变模型为:研究其平衡点的指数稳定性.通过用压缩影像原理证平衡点存在唯一,建立新的李雅普诺夫函数证的其平衡点的全局指数稳定性,其中所含时滞既不只是纯连续的,也不只是纯离散的.在原有文献的基础上改进时滞,推广了相关文献的结果.更多还原

【Abstract】 With the development of modern society, neural networks is widely used in engineering,astronavigation,economy, financial etc.In most cases,many problems are solvedmore practically by delayed neural networks than neural networks. Great achievementshave been given by the respective researchers, especially about stability of fixed pointsand periodic solutions of neural networks with delayed, many specialists and scholarsapply themselves to the research of theory and achieve many perfect productions. Inthis paper, we perform re-searches of the stability of several of networks with delayedThe main contents of this paper include:In the first chapter ,the model aswas studied. Based on Lyapunov functional method, we study the global exponential stability for delayed impulsive cellular neural networks (DCNN)and give a newsufficient condition.exponential stability and periodicity of the model are investigatedIn the second chapter,firstly dynamics of a class of retarded impulsive differentialequations (IDE)are studied, which generalizes the delayed cellular neural networks (DCNN)and delayedbidirectional associative memory (BAM) neural networks. The approaches are basedon Banach’s fixed point theorem, matrix theory and its spectral theory.Secondly the global exponential stability stability and periodicity for a class ofreaction-diffusion differential equations with Dirichlet boundary conditions as andwhich are address by constructing suitable Lyapunor functional and utilizing someinequality techniques.In the third chapter, a class of high-order neural networks with time delays andimpulsive effects asthe global exponential stability and periodicity are investigated for it. Some sufficientconditions are derived for checking the global exponential stability and the existenceof periodic solution for this system based on Halanay Inequality, induction and fixedpoint theorem.In the fourth chapter, a class of general Cohen -Grossberg neural networks withimpulsive is studied,based on the method of Lyapunov function, which is model with discrete and distributedelay.sufficient conditions on global exponential stabitity are given.Moreover,comparisionsandmade with earier findings.更多还原