The Boundary Value Problems For Second-order Ordinary Differential Equations In Banach Spaces And The Synchronization Of Fuzzy Cellular Neural Networks

This paper consists of five parts, in chapter one, we first introduce the emer-gence,development,actuality and the problems we will study of differential equations and cellularneural networks.In the past twenty years, the theory of ordinary differential equations in Banach spaces hasbecome important. It became a powerful tool to solve practical problems in physical, biochemical,remote control and many other fields .On the other hand, multi-point boundary value problemsarising from applied mathematics and physics have received a great deal of attention. However,few results can be found in the literature concerning multi-point boundary value problems inBanach spaces.In the second chapter of this article, we have done a detailed comparative study on the multi-point boundary value problems in Banach spaces. By using the Sadovskii fixed point theorem,we study the existence of solutions for the second-order multi-point boundary value problem inBanach space.We introduced impulse into the equations, to make it more specific.1990, Pecora and Carrol introduced a new concept-synchronization of coupled chaotic sys-tems, It has proved that synchronization is an effective method .In order to illustrate its effec-tiveness, in the fourth chapter, we presented the synchronization of delayed fuzzy cellular neuralnetworks. However, the real world phenomenon is daedal. It has been observed that when asynchronization method is applied to a dynamic neural network, even smallest perturbations maybring about the failure of synchronization scheme. So, in chapter five, we discussed the synchro-nization of reaction-diffusion delayed non-autonomous fuzzy cellular neural networks.Lastly, a summary of this paper is made and further research directions are put forward.