几类具变时滞的神经网络模型的动力学研究

【作者】 彭水军；

【导师】 黄立宏；

【作者基本信息】 湖南大学 ， 应用数学， 2002， 硕士

【摘要】 本篇论文共由四章组成。 第一章概述了问题产生的历史背景和本文的主要工作。 在第二章中，讨论一类推广的具变时滞和变系数的双向联想记忆(BAM)神经网络模型的渐近状态。这里，信号传输函数f_i，g_i(i=1，2，…，n，j=1，2，…，m)是R→R上的连续函数，且满足Lipschitz条件。我们利用M-矩阵理论、微分不等式分析技巧和构造Lyapunov泛函方法，建立了神经网络系统(E)与时滞无关的全局指数稳定性判据和保证周期解的存在唯一及其稳定性的几个充分条件；同时考虑了系统(E)退化为常时滞和常系数情形的全局渐近稳定性问题，这些结果较大地改进和推广了一些已知的结果。 第三章研究了具可变时滞的BAM细胞神经网络模型的周期解与稳定性问题，获得了保证系统的平凡解收敛的充分条件以及关于周期解的存在与稳定性的结论，所得结果对于连续的BAM神经网络的设计和应用具有一定的指导意义。更多还原

【Abstract】 This paper is composed of four chapters.In Chapter 1, we introduce the historical background of problems which will be investigated and the main work of this paper.In Chapter 2, by using M-matrix theory, some analysis techniques and constructing suitable Lyapunov functionals, we investigate the convergence of solutions and the existence and uniqueness of periodic solution for system:where ft and g, are the propagational signal functions defined onR. Several sufficient conditions guaranteeing the neural exponential stability as well as the existence and stability of periodic solution of the neural network are obtained. The global asymptotically stability of the corresponding neural network models with constant delays and coefficients is studied too. Our results improve and generalize some known results.In Chapter 3, the periodic oscillatory solutions and the global stability are studied for a class of continuous bi-directional associative memory neural network models with variable delays, and some simple and new sufficient conditions are given ensuring global exponential stability and the existence of periodic solutions of the neural nework. These results have important leading significance in the design and applications of global exponential stable BAM networks and periodic oscillatory BAM networks.更多还原