Dynamic Analyses On Delayed Shunting Inhibitory Cellular Neural Networks With D Operator

In recent years,the research on the theory and application of neural network model has been widely concerned by many scholars.Because the dynamic behavior of most neural network models is significantly affected by time delays,it is necessary to study the dynamics of neural network models with time delays.Meanwhile,the neutral time delay neural network with the D operator can objectively describe practical problems in the fields of pattern recognition,image processing,and optimization design.Therefore,the importance of research on the dynamics of this kind of network model has become increasingly prominent,which is urgent for people to study deeply.In this thesis,the related theories of functional differential equations,fixed point theorem,Lyapunov functional method and differential inequality techniques are applied to study the convergence of two kinds of D operator shunting inhibitory cellular neural networks with different time delays.The main research contents includes the existence and global exponential stability of positive almost periodic solutions and weighted pseudo almost periodic solutions of the models.The obtained conclusions supplement and improve the results in the existing literature.The full text consists of four chapters.In Chapter 1,the research background and general situation of shunting inhibitory cellular neural networks are introduced.The work to be studied in this paper is briefly explained,and the basic marks and definitions needed in this thesis are listed.In Chapter 2,a class of D operators-type shunting inhibitory cellular neural network system with bounded time-varying delays and unbounded continuous distributed delays is studied.Firstly,we prove the global existence of positive solutions of the given system.Secondly,by using differential inequality techniques and Lyapunov functional method,the relevant criteria for the existence of positive almost periodic solutions and global exponential stability of the system are established,which complement the corresponding works of some existing literature.In addition,the correctness and feasibility of the actual network model are verified by examples and numerical simulations.In Chapter 3,a class of D operators-type shunting inhibitory cellular neural network system with proportional time delays is studied.First,we prove the existence and uniqueness of weighted pseudo almost periodic solution of the system by using fixed point theory.Secondly,by using differential inequality technique and Lyapunov functional method,we obtain a new sufficient condition to guarantee the global generalized exponential stability of the weighted pseudo almost periodic solution of the considered model.The obtained results improve and supplement the corresponding results in the literature.At the end of this chapter,we also give a numerical simulation to support the proposed approach and demonstrate the correctness of the main conclusions.In Chapter 4,our research works and the prospect of our future research are summarized.