一类神经网络模型的稳定性分析

研究了一类神经网络,包括Hopfield神经网络和细胞神经网络,从神经网络的互连矩阵以及神经元输入输出的激励函数出发,通过研究特殊矩阵以及单调有界函数,利用Brouwers’不动点理论和构造Lyapunov函数的方法讨论神经网络平衡点的存在唯一性和全局指数稳定性以及指数的收敛速率,获得了一些充分条件以保证神经网络的平衡点的存在性、唯一性和全局指数的稳定性,并给出了一些条件下指数收敛速率的估计值.

The Global Exponential Stability of Certain Neural Network Model

In this paper,we study a variety of neural networks,including Hopfield neural network and cellar neural network.We start from the neural network's interconnection matrix and the neurons' input and output activation function,through studying the special matrix and bounded monotone function,as well as taking advantage of Brouwer's fixed point theory and the method of constructing Lyapunov function,the uniqueness of the existence of the neural network's equilibrium point,the global exponential stability and th...