随机延时神经网络的吸引子和分岔

项目名称： 随机延时神经网络的吸引子和分岔

项目编号： No.11271295

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 万立

作者单位： 武汉纺织大学

项目金额： 60万元

中文摘要： 神经网络理论已经应用于组合优化、模式识别、信号处理、计算机视觉、通信等领域。非线性动力学问题是神经网络理论的一个重要组成部分。针对随机神经网络的吸引子和分岔存在性条件及其规律等问题，本项目通过随机微分方程、随机动力系统、随机分析等理论和方法，以Hopfield 神经网络、细胞神经网络、Cohen-Grossberg神经网络、双向联记忆神经网络等为主要研究对象，首先研究这些网络的吸引子和分岔的存在条件；其次，研究这些网络在具有反应扩散项时的吸引子的存在条件；最后分析延时、随机项对神经网络吸引子和分岔的影响程度，并通过数值模拟验证结果的正确性。本项目的研究成果不仅揭示神经网络动力学行为的复杂性，探索神经网络的演化机制和内在规律, 促进神经网络等相关领域的理论和应用研究的发展，而且有助于理解神经网络数学理论的依据和背景，为神经网络的设计开发和应用提供基本思想及可能途径。

中文关键词： 随机神经网络；延时；吸引子；；

英文摘要： The theory of neural network has been applied in combinatorial optimization, pattern recognition, signal processing, computer vision, communication and other fields. Nonlinear dynamical problem is an important part of the theory of neural network. For some problems including the existence conditions and rules of attractor and bifurcation of stochastic neural network, by using the theories and methods of stochastic differential equations, random dynamical system and stochastic analysis, this project takes Hopfield neural network, cellular neural network, Cohen-Grossberg neural network, bidirectional association memory neural network as the main research objects, firstly studies the existence conditions of attractor and bifurcation; secondly studies the existence conditions of the attractor of these networks with reaction-diffusion term; finally analyzes the effects of delay, stochastic term on the attractor and bifurcation of neural networks. The research results of this project not only reveal the complexity of dynamical behaviors of stochastic neural network, explore the evolution mechanism and internal rules of neural network and promote the development of theoretical and applied research of neural network and other related areas, but also contribute to the understanding of mathematical theory basis and backgr

英文关键词： stochastic neural network；delay；attractor；；