Stability Analysis On Saturated Impulsive Cohen-grossberg Neural Network

With the wide applications of Cohen-Grossberg neural network,the dynamical issues of the network have attracted worldwide attention and more scholars have studied the network model.Lots of profound research results have been obtained.Because the impulsive information transmission is an inherent property of biological neurel network,the impulsive neural network has been a hot topic in the field of artificial intelligence in recent years.Meanwhile the saturations exist in inputs and outputs of biological neuron or physical system.Therefore,the research of impulsive neural networks with saturation has great theoretical and practical value.In this paper,the stability of Cohen-Grossberg neural network with impulsive inputs is studied by theories of impulsive differential equation,saturated control,technique of inequalities.Sufficient conditions for asymptotic stability are obtained.The main research contents include the following two aspects:(1)The stability of Cohen-Grossberg neural network with saturated impulsive inputs is analyzed.In view of the fact that the inputs cannot be infinite,the symmetric saturation is introduced into the impulsive Cohen-Grossberg neural network and the Lyapunov method,convex analysis and matrix inequality are applied to analyze the stability.Not only the full state constraint inputs are introduced,but also the partial state constraint inputs are informed.In addition,the stability of the the delayed impulsive network with the saturated inputs is analyzed by the similar method.The effectiveness and feasibility of the method are verified by numerical simulations.(2)The stability of the time-varying impulsive Cohen-Grossberg network is analyzed.Suppose each collision plane is continuous and monotonous,and the condition of the intersection of the derived trajectory and the given collision plane at most twice is discussed.Then,in combination with Lyapunov function analysis,the asymptotic stability is further studied for the impulsive Cohen-Grossberg network,and the conditions for the stability of the impulsive network are obtained.Based on the results,the appropriate collision surfaces and impulses can be designed to insure the time-varying impulsive neural network be asymptotically stable at the origin.Two numerical simulations verify the validity of the theoretical results.