广义非线性网络系统的定性与稳定性研究（Ⅰ）

STUDY ON QUALITATIVE AND STABILITY FOR SINGULAR NONLINEAR NETWORK SYSTEM

本文研究了更具一般形式的广义非线性网络系统（这类系统包含了细胞神经网络和Ｈｏｐｆｉｅｌｄ网络），给出了系统全局渐近稳定性和绝对稳定性的定义及判别条件。利用隐函数定理及Ｐ０矩阵族性质，讨论了平衡点存在及唯一性问题，并给出了平衡点存在且唯一的充分条件。

This paper considered rather general class of network system, called singular nonlinear network system. This system includes cellular neural networks and Hopfield networks. The definition of global asymptotic stability and absolute stability and criterion theorem for them are given. The problem of existense and uniques for equilibrium point is studied by using implicit function theorem and the properties of P 0 Matrices. At last, the boundedness of solution is considered by employing the frequency domain method and variation of constants formula.