Two Types Of Travelling Wave Solution Of Diffusion System Research And The Type Of Global Exponential Synchronization Analysis Of Fuzzy Neural Network

This paper consists of four parts, in chapter one, we introduce thebackground, the problems and the innovation of two different kinds of reaction-diffusion system and one kind offuzzy cellular neural networks.For nonlinear reaction-diffusion traveling wave solutions areimportant since they determine the long term behavior of othersolutions in many situations. In fact, many powerful methods have beenused to study the traveling wave solutions for reaction-diffusion systems.In2010, Qintao Gan investigated the existence of traveling wavesolutions to a three-species food chain model with spatial diffusion andtime delays by using Schauders fixed point theorem. In chapter two ofthis paper, we investigate a n-species food chain model with spatialdiffusion and time delays.As we all know, the speed of a traveling wave determines howquickly specie converges to a stable state. So the research on theexact minimum wave speed has been paid more and moreattentions. So, in chapter three, we investigate the minimum wavespeed for a generalized Lotka-Volterra reaction-diffusion competitionmodel with time delays.In the last two decades, cellular neural networks(CNN) has beenintensively studied and applied in many areas. As an importantaspect, synchronization of cellular neural networks, especiallysynchronization of coupled cellular neural networks has becomemore and more significant. Many results on synchronization of coupledCNN have been obtained. Since time-delay and fuzzy control can make the system moreaccurate and much more closer to the actual situation, in chapter four,we investigate the exponential synchronization of the coupled fuzzycellular neural networks with time delays. An example is finallyintroduced to visualize the feasibility and effectiveness of the method.