【作者】 李翠波；

【导师】 王林山；

【作者基本信息】 中国海洋大学 ， 应用数学， 2007， 硕士

【摘要】 人工神经网络是目前国内外关注的一个非常活跃的研究领域,它在智能控制、模式识别、图像处理、非线性优化计算、传感技术、机器人等众多领域都有广泛的应用。在实际应用中,人们通过电子电路来实现神经网络的功能,由于受人为因素以及神经元放大器有限转化速度和技术水平等客观因素的影响,时滞现象是不可避免的。时滞现象,其不但会降低网络的传输速度而且常常会导致网络的不稳定,所以,具有时滞的神经网络系统的动力行为就尤为重要。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。静态神经网络模型,它将神经元外部状态作为变量研究,在某些递归神经网络中有广泛应用,例如ReBP网(Recurrent back-propagation networks)、CNNs网(Cellular neural networks)、BSB网(Brain-state-in-a-box type networks)等。现在关于递归神经网络的研究大多集中于局域神经网络模型,静态神经网络模型的动力学性质还未被深入讨论。在目前有关时滞静态神经网络系统动力学行为的研究成果中,绝大部分局限于研究常时滞情况,对变时滞神经网络系统的研究工作尚不多见。本文主要研究了变时滞静态神经网络的一些动力行为。本文的安排如下:第一章是概述,简单介绍了人工神经网络,涉及本文将要用到的定义及定理;第二章的内容是运用非负矩阵性质和不等式技巧,研究了变时滞静态神经网络存在不变集和周期吸引子的充分条件,并对周期吸引子的存在范围进行了估计。第三章的内容是利用矩阵不等式的分析技巧和Banach空间中不动点定理,通过构造李雅普诺夫函数,研究变时滞静态神经网络的概周期解,得到了变时滞静态神经网络概周期解存在性,唯一性和全局指数稳定性的充分条件。第四章则利用拓扑度理论,Young不等式及矩阵不等式的分析技巧,研究变时滞静态神经网络平衡点的存在性和全局指数稳定性,得到一系列充分条件。更多还原

【Abstract】 Artificial neural network is a very active research area in these years, it is applied in pattern recognition、automatic-control systems、optimization、image processing、signal processing、associative memories and so on . In practical applications, people carry out the functions of the ANN by using electronic. Time delays are inevitably encountered in neural networks because of the artificial factors、the finite switching speed of amplifiers and technical level, and so on. Time delays not only reduce the velocity of transmission, but also cause instability and poor performance of neural networks. So it is important to research dynamical behavior of neural network with time delays.Basing on the different basic variables, the mathematical model of neural networks can be divided into two types—local field neural networks model and static neural networks model. Static neural networks model research outer state of the neuron and it is applied in several recurrent neural networks, for instance Recurrent back-propagation networks、Cellular neural networks、Brain-state-in-a-box type networks, and so on. Most researchers about neural networks focused on the local field models, few paid attention to the static models.In the results of dynamical behavior of static neural network with time delays, most are about constant time delays, few about time-varying delays. In this paper, dynamical behavior of static neural network with time-varying delays will be investigated.This paper is organized as follow. Chapter 1 introduces the general knowledge and presents several important definitions and theorems. In chapter 2, some sufficient criteria of the invariant set and periodic attractor are derived. Particularly, we have provided an estimate on existence range of periodic attractor by using the properties of nonnegative matrices and differential inequality technique. In chapter 3, some sufficient criteria of the existence, uniqueness and exponential stability of the almost periodic solution are derived by using the fixed point theorem of Banach space, nonnegative matrices theory and differential in equality technique. In chapter 4, some sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solution for such delayed neural networks by using the topological degree theory, Young inequality and nonnegative matrices theory.更多还原