【作者】 赵永昌；

【导师】 王林山；

【作者基本信息】 中国海洋大学 ， 海洋信息探测与处理， 2010， 博士

【摘要】 近二十年来,人工神经网络的理论和应用研究引起科学工作者的极大兴趣,并成为非线性科学领域的研究热点之一,究其原因,这主要因为人工神经网络是非线性信息处理系统,有着广泛的应用。神经网络可分为工程神经网络和数学神经网络。工程神经网络以硬件或软件形式实现某种信息处理功能；数学神经网络是由工程神经网络提出的数学模型,通常称为递归神经网络,主要是研究其动力学特征,为工程神经网络提供理论支持和保证。根据系统基本变量选取的不同,递归神经网络的数学模型可分为静态神经网络和局域神经网络。目前关于递归神经网络的研究大多集中于局域神经网络模型,而静态模型的研究相对较少。然而,许多重要的神经网络却归结于静态模型,因此,研究静态模型具有重要的理论意义和实用价值。在人工神经网络的电子实现中,由于网络神经元放大器的有限转化速度问题,时滞是不可避免的.同样,脉冲现象和随机扰动在神经网络实现过程中是不可避免的,是广泛存在的,且很多情况下,它们往往和时滞在同一个系统中出现,因此,本文研究时滞静态递归神经网络同时,考虑了脉冲、随机扰动对神经网络的影响。本文主要由7章组成,主要内容如下：第一章,简介了人工神经网的研究现状,概述了静态递归神经网络动力系统的研究背景和发展状况,介绍了本文的主要工作。第二章,运用不动点理论、M-矩阵的性质、李雅普诺夫函数结合不等式技巧研究了变时滞静态递归神经网络的周期解的存在性及其全局鲁棒指数稳定性,以及分部时滞静态递归神经网络概周期解的存在和全局指数稳定性,分别得到了相应问题稳定性的判定条件,推广了相关研究的结果。第三章,利用Lyapunov-like稳定性定理及不动点原理研究了脉冲时滞静态递归神经网络平衡点的稳定性及周期解的稳定性,得到判定脉冲静态递归神经网络稳定的条件,并举例说明条件的正确性。第四章,考虑随机扰动对静态递归神经网络动力学行为的影响,利用无穷小算子,Ito公式及半鞅收敛定理,分别研究了随机变时滞静态递归神经网络、分布时滞静态递归神经网络,得到了考虑随机扰动时滞静态递归神经网络的全局几乎指数稳定性的判定条件。第五章,研究了马尔可夫调制的静态递归神经网络,及同时考虑随机扰动和马尔可夫切换的时滞静态递归神经网络模型,利用线性矩阵不等式,有限状态空间马尔可夫链的性质及Lyapunov—krasovskii函数,得到了系统全局指数稳定性的的判定条件。第六章,首先利用广义的Halanay不等式研究具有反应扩散时滞静态递归神经网络的全局指数稳定性问题,然后结合马尔科夫链的性质研究了马尔可夫调制的反应扩散时滞静态递归神经网络的稳定性。第七章,最后,对本文所研究的内容和主要结果进行了总结,并对研究工作的前景进行了展望。更多还原

【Abstract】 In the recent decades, more and more scientific scholars are interested in the theory and application of artificial neural networks because of its nonlinear processing system, which is one of the most active researches in the area of the nonlinear science. Artificial neural networks can be divided into two types, one is the engineering neural networks which are used for information processing by software or hardware, the other is mathematical neural networks which is mathematical model of the former and usually called recurrent neural networks. Investigations of dynamical characteristic of the latter can provide theoretical support and guarantee for the former. Based on the difference of basic variables, the mathematical models of recurrent neural networks can be divided into two types—local field recurrent neural network models and static recurrent neural network models. Most current research about recurrent neural networks focused on the local field models, few paid attention to the static models. However, static models are widely representive. Many useful neural networks are modeled as static models. It is important to investigate the static models.In the realization of electronic neural networks, time delays are unavoidable due to the finite switching speed of amplifiers. For this reason, classes of static recurrent neural networks with time delays are investigated in this paper. Like the time delays, impulses and stochastic perturbations exist in the realization of electronic neural networks, they often exist in the same system with time delay. So in this paper, time delays, impulses and stochastic perturbations are considered in the investigated static recurrent neural networks.This paper is composed of seven chapters and main results are described as follows:In Chapter one, the historical background and the recent development of static recurrent neural networks is introduced, and the main results of this paper are also briefly introduced. In Chapter two, by using the fixed point theory, properties of matrix M, the Lyapunov function and differential inequality, firstly, the existence and global robust exponential stability of periodic solution for the static neural network with time-delays is investigated, after that, the existence and global exponential stability of almost periodic solution for the static neural network with distributed delays is investigated, and some sufficient criteria are established, which improves and generalizes some known resultsIn Chapter 3, the author investigates the global exponential stability of the equilibrium point and periodic solutions for impulsive static neural networks with time delays or distributed delays by using the fixed point theory and Lyapunov-like stability theorem, and two numerical examples are given for illustration of the theoretical results.In Chapter 4, stochastic perturbations to the stability property of static recurrent neural networks with discrete and continuously distributed delay are considered. By establishing L-operator inequality, Ito’s formula and semimartingal convergence theorem, we obtain some sufficient criteria to check the almost sure exponential stability of the each system.In Chapter 5, the author investigates the system of the static recurrent neural networks with discrete delay and Markovian switching and the system of the stochastic static recurrent neural networks with distributed delay and Markovian switching, sufficient criteria to check the global exponential stability of the each systems are established by using a new Lyapunov-krasovskii functional, linear matrix inequality and the properties of Markovian chain.In Chapter 6, first, the exponential stability of the delayed static reaction-diffusion recurrent neural networks is investigated by generalized Halanay inequality, after that, due to the properties of Markovian chain, a sufficient condition to check the exponential stability of the delayed static reaction-diffusion recurrent neural networks with Markovian switching is obtained.In Chapter 7, the studying contents and the main results of this paper are briefly summarized, further more, some research prospects are also proposed.更多还原