The Study Of Dynamics On Three Kinds Of Differential Equations Based On Perturbation Incremental Method

In recent years,with the further study of nonlinear systems and the proposal of some nonlinear quantitative analysis methods,the perturbation incremental method,which is a quantitative analysis method for nonlinear systems,is becoming a hot topic.In order to extend the applications of this method,the dynamic behaviors of Rayleigh system,quadratic reversible system and nonlinear conveyor belt system are studied quantitatively by employing perturbation incremental method in this paper.The zero order perturbation solution obtained from the perturbation part is taken as the initial solution of the incremental part.In the incremental part,the analytical approximate expressions of the limit cycles under certain parameter conditions are obtained,and the numerical simulations of the systems are carried out with MAPLE and MATLAB to verify the results.The full paper has been divided into six chapters:The first chapter introduces the relevant research backgrounds and research status,as well as the main research contents of this paper.The second chapter gives some preliminary knowledge.In Chapter 3,the problem of limit cycles for a class of Rayleigh systems is discussed with two parameters.The zero order perturbation solution of the limit cycle and the initial value of parameter ? are obtained.After incremental iterations,the analytical approximate expressions satisfying certain accuracy and values of ? are derived.In Chapter 4,we apply the perturbation incremental method to study the analytical approximate solutions of limit cycles for a class of quadratic reversible system,and obtain the analytical approximate expressions of limit cycles under certain conditions.In Chapter 5,the dynamic behaviors of a class of nonlinear conveyor belt system are discussed by combining the perturbation incremental method with engineering application.These limit cycles are discussed by making some appropriate changes to the use of the perturbation incremental method,and analytical approximate expressions are obtained.By comparing with the fourth order Runge-Kutta method,it is proved that the result obtained by perturbation increment method is effective.In Chapter 6,the summary and prospect of this paper are given.