【作者】 袁少良；

【导师】 李雪梅；

【作者基本信息】 湖南师范大学 ， 应用数学， 2009， 硕士

【摘要】 本硕士学位论文利用中心流定理和规范型理论,对带自反馈的环状时滞细胞神经网络的稳定性和Hopf分支进行了分析,其中中心流定理起降低维数的作用,而规范型理论则是将所研究的问题尽可能在等价意义下从形式上予以简化,全文共分三章.第一章简单介绍该问题研究的背景和发展的现状,以及它的广泛应用和研究工作的意义.第二章讨论单向环状带自反馈的时滞细胞神经网络模型:的稳定性和Hopf分支,得到了一些相关的结果,并就这些结果做了数值模拟实验进行验证.第三章讨论双向环状带自反馈的时滞细胞神经网络模型:的稳定性和Hopf分支,得到了一些相关的结果,并就这些结果做了数值模拟实验进行验证.在第二章和第三章中,每章由三部分组成,第一部分为引言和模型部分;第二部分主要分析平凡解的线性稳定性,给出几个判断网络稳定性和不稳定的充分条件,讨论分支的存在性,并以自反馈时滞作为分支参数,给出分支值的计算公式;第三部分利用中心流定理和规范型理论来确定分支方向、分支周期解的稳定性等性质,给出例子以及数值模拟实验验证本文主要结果.更多还原

【Abstract】 This thesis analyzes the Hopf bifurcation and stability of annular delayed neural networks with self-connection, by applying the center manifold theorem and the normal form theory, in which the center manifold theorem is applied to reducing dimensions, while the normal form theory for simplifying the form of our models.In Chapter 1, we briefly introduce the background and the recent development of the issue we researched , in which its applying and the purpose of the investigation are denoted, too.In Chapter 2, we discuss the stability and bifurcation of an annular delayed neural network with self-connection:We obtaine some relevant results, and then make the numerical simulation experimentsto verify them.In Chapter 3, we investigate the stability and bifurcation for a class of threeneuronnetwork with two delay and self-feedback:We obtaine some relevant results, and then make the numerical simulation experimentsto verify them.In Chapters 2 and 3, each chapter consists of three parts, the first part is for the introduction and model ; the second part mainly analyzes the linear stability of trivial solution, gives some sufficient conditionsstability and instability ,discusses the existence of a branch and gives the formula for calculating the value of branch through regarding the self-feedback delay as the parameter of branch ; the third part uses the center manifold theorem and the normal form theory to determine the branch direction and stability of periodic solutions nature, and gives examples of numerical simulation experiments to verify the main results of this paper.更多还原