Stability Analysis For A Class Of Delayed Neural Networks With Homogeneous Activation Functions

Recently the dynamics of neural networks as an indispensable tool for solving various technology and science problems have drown an increasing attention by numerous scholars. There are four chapters in this paper and the principal part of this article is divided into two chapters:The first part is the introduction, which mainly introduces the background, the research status at home and abroad and related definitions and lemma.In section 2, the problem of asymptotic stability analysis is investigated about a class of delayed neural networks with homogeneous right-hands sides. Under the assumption that the trivial solution of delay free system is asymptotically stable and the activation functions are homogeneous, it is proved that the zero solution of delayed neural network is asymptotically stable for arbitrary nonnegative delay. By constructing a Lyapunov function and employing the nature of homogenous function, a new delay-independent asymptotically stability condition of the neural network with delay is obtained.In section 3, the existence, uniqueness and the global asymptotic stability of the equilibrium point for a class of delayed neural networks with impulsive effects is investigated. It is assumed that the activation functions are Lipschitz continuous and homogeneous. By means of Homeomorphism mapping theorem and Lyapunov stability theorem, the new sufficient conditions are derived to guarantee the existence, uniqueness and the global asymptotic stability of the equilibrium point for delayed impulsive neural networks are obtained.The last part summarizes the methods used in this paper and points out the future research.