On The Dynamical Behaviors In Nonautonomous Periodic Cellular Neural Networks With Impulses

Since neural networks have enormous potential in wide varieties of appli-cations, many specialists and scholars apply themselves to the research of thetheory and achieve many perfect productions. In this paper, we perform re-searches of the stability and existence of periodic solution of impulsive cellularneural networks (ICNNs). The main contents of this paper include: the existenceof periodic solution and the stability analysis for a class of first-order and a classof second-order CNNs with time-varying delays and impulses, respectively.The main contents in this paper can be summarized as follows:1. Firstly, in the first section of the first chapter, we introduce the devel-opmental process and significance of neural networks. In the following section2 we introduce the models of cellular neural networks. In section 3, we intro-duce the research results for impulsive cellular neural networks. In section 4, theorganization of this paper is given.2. In the second chapter, we mainly analyze a class of first order impulsivecellular neural networks with delays. In this section we discard the demand thatthe activation functions must be di?erential, monotone and bounded and onlyrequest them to be Lipschitz continuous. Particularly, we do not require that theactivation functions be Lipschitz continuous in the proof of existence of periodicsolution. By using the continuation theorem of coincidence degree theory andconstructing appropriate Lyapunov functional, su?cient and realistic conditionsfor existence and global exponential stability of periodic solution are established.3. In the third chapter, the high-order CNNs model with impulses to whichis scarcely referred in the internal and external literatures will be investigated. As the high-order neural networks are more complex than the first-order ones,by far, the activation functions in systems are usually assumed be bounded andmonotonic increasing even. we assume that the activation functions are Lipschitzcontinuous, but we do not require that all activation functions be bounded.Consequently, the su?cient conditions for the global exponential stability ofthe system and existence of periodic solution of the system will be obtainedby using constructing appropriate Lyapunov functional and generalized Halanayinequality. Therefore, our results is more general in reality, and complete andimprove the pervious results.4. In the fourth chapter, conclusion and discussion are given...