Periodic Oscillation and Exponential Stability of a Class of Competitive Neural Networks

摘要

In this paper, the periodic oscillation and the global exponential stability of a class of competitive neural networks are analyzed. The competitive neural network considered includes the Hopfield networks, Cohen-Grossberg networks as its special cases. Several sufficient conditions are derived for ascertaining the existence, uniqueness and global exponential stability of the periodic oscillatory state of the competitive neural networks with periodic oscillatory input by using the comparison principle and the theory of mixed monotone operator and mixed monotone flow. As corollary of results on the global exponential stability of periodic oscillation state, we give some results on the global exponential stability of the network modal with constant input, which extend some existing results. In addition, we provide a new and efficacious method for the qualitative analysis of various neural networks.