Periodic Solution And Stability Of Discrete-time Neural Networks

Since cellular neural networks were introduced by Chua and Yang in1990[1,2],they have been successfully applied, and became a popular research topic in the fledof application mathematics. In1992, H.Harrer and J.Nossek introduced discrete-timecellular neural networks, and discrete-time neural networks have attracted the attentionof many researchers. However, we see, for discrete neural networks, up until now, studyworks are very few. In this paper, Our main purpose is to investigate the dynamicalbehaviors of discrete-time neural networks. The main contents in this paper can besummarized as follows:The section1is introduction, in which we introduces research background, purposeand signifcance of discrete-time neural network, and then given the research status andresults of discrete-time neural network. Finally, the organization of this paper is alsopresented.In section2, a class of discrete-time Cohen–Grossberg neural networks with delaysand impulses is investigated. some sufcient conditions have been obtained to ensure thatdiscrete neural networks have only one periodic solution and all solutions of this systemconverge to the periodic solution by using Lyapunov functional method and applyingMawhin’s continuation theorem. Finally, an example with numerical simulation is givento demonstrate the efectiveness of the obtained results.In section3, we study convergence behaviors of delayed discrete cellular neural net-works without periodic coefcients. Some sufcient conditions are derived to ensure allsolutions of delayed discrete cellular neural network without periodic coefcients convergeto a periodic function, by applying mathematical analysis techniques and the propertiesof inequalities. Finally, some examples showing the efectiveness of the provided criterionare givenIn section4, the stability of discrete-time impulsive delay neural network with and without uncertainty is investigated. some sufcient conditions are given to guarantee ex-ponentially stability of uncertain discrete-time neural network with delay and impulsesby using Lyapunov functions, linear matrix inequalities(LMIs)and Razumikhin-type the-orems. Finally, several examples with numerical simulation are given to demonstrate theefectiveness of the obtained results.