Stability And Periodic Solution For Several Kinds Of Cellular Neural Networks

The cellular neural network has grown fast in recent years,it has been widely used in many important areas.At the same time,the real world also ask cellular neural network to solve more and more problems,such as impulsive phenomenon. However,the results about the dynamic properties of cellular neural network with impulse are still relatively rare.For this purpose, this is composed of four chapters,which mainly study the stability and periodicity of solutions for several kinds of cellular neural networks.In chapter one,we introduce the development and research of the cellular neural network. Our works also are given in this thesis of Master.In chapter two,we study the existence and grobally exponentially stable of equilibriumpoint for this impulsive cellular neural network with time delaysWe improve some known result,and obtain some new result by M Array Theory and Lyapunov Method:If the following conditions are satisfied(H₁) there exist positive constantsδ: 0 <δ< (?) {r_i}, such that(H₂) surpose thatη_m = ||P_m + E||₁,λ(?) <δ, n_m≥e^δτ.in thatβ= (?);(i = 1, 2, 3…n), then the system has a unique grobally exponentially stable equilibrium point, it's exponential rate isδ-λ.Chapter three mainly considers the existence and grobally exponentially stable of periodic solution for this impulsive cellular neural network with time delays by using coincidence degree theory.We establish two new criterias.Also,they are new for cellular neural network with no impulsive. Surpose that(H₁) r_i>0,a_ij(t),b_ij(t),u_i(t) andÏ„_ij(t)≥0 are continuous and T- periodic functions for the arguments in the R,(H₂)exist a postive number k such that t_m+k= t_m + T,I_i(x,(t_m + T)) = I_i(x,t_m),(m = 1,2,3…),(H₃) |I_im|≤M, (?)t_m∈R,(H₄) 1 - rT > 0.are satisfied,then this system must have one periodic solution. The other theorem is in the chaper three.In the last chapter,we investigate the existence of periodic solution for this cellular neural network with threshold nonlinearity.in whichWe improve the method and obtian another case for this classes of model.