Function Cascade Synchronization Of Fractional Chaotic System And Local Wave Solutions Of Nonlinear Equation

With the development of technology,nonlinear science has developed rapidly and involved in almost all scientific and social fields,such as physics,mechanics,life science,engineering technology and so on.Chaos,soliton and fractal are three important branches of nonlinear science.The study of them is of great significance not only to the theory of mathematical physics itself,but also to the application in real life.In this dissertation,based on symbolic-numeric computation software,the synchronization of fractional chaotic system and the exact solutions of nonlinear soliton equation are studied.For chaos synchronization,we propose the function cascade synchronization method and the delay function cascade synchronization method of fractional order chaotic system,and give their automatic reasoning format;for exact solutions,we mainly construct the local wave solutions of some important nonlinear soliton equations.This thesis is divided into four chapters.The details are as follows:In Chapter 1,we mainly introduce the history and progress of chaos synchronization and soliton theory.The related research work of experts and scholars at home and abroad is introduced.Finally,we give the structure of this thesis.In Chapter 2,based on the stability theory,we propose the automatic reasoning format of the function cascade synchronization method of fractional order chaotic system,and study the function cascade synchronization of fractional order unified chaotic system,fractional order hyperchaotic Chen system.The effectiveness of the proposed method is verified by numerical simulation.In Chapter 3,we propose an automatic reasoning scheme for the delay cascade function synchronization of fractional order chaotic systems.Based on stability theory,we design appropriate controllers to realize the delay cascade function synchronization of fractional order Lü system.The effectiveness of the algorithm is verified by numerical simulation.In Chapter 4,by using the long wave limit method and restricting the complex conjugate condition to the N-soliton solution,we construct the localized wave solutions of the 2+1dimensional Sawada-Kotera equation and KP equation,including the N-soliton solution,the M-lump solution,the higher-order breather solution and the localized interaction wave solutions.Finally,the properties and dynamic behaviors of these solutions are studied by means of numerical simulation and graphic analysis.Finally,the summary and outlook of the dissertation are given.