Bifurcation And Chaos Of Phase-Shift Nonlinear System

The dynamical analysis of bifurcation and chaos is one of the frontier problem in the study of nonlinear dynamical systems. Based on the results we have obtained, the mechanism of the complexity is discussed by applying the modern nonlinear analytical methods to the systems. The details of the influence on the dynamical behavior caused by the physical parameters and the initial conditions are also explored in this thesis in order to reveal the quality of the complexity , which may provide the theoretical basement for solving practical engineering problems, such as nonlinear modeling parametrical identification and failure diagnose.Firstly, the average equation under first,and second order of Van der pol-Mathieu-Duffing system are obtained through theatric methods. According to the stability criteria, the physical parameter plane is divided into different regions, associated with different types of steady state solutions, which are proved by employing numerical methods.Secondly, the bifurcations of Van der pol-Mathieu-Duffing system with different parameter are analyzed through numerical methods, especially the effect caused by the phase-shift are discussed. The bifurcation diagram in different parameter plane and poincare maps are obtained. From that, different bifurcation type are get. From that, routes to chaos are obtained in the evolving process of the movements of system.Thirdly, the heterclinic orbit bifurcations are discussed in detail by applying the global perturbation method developed by Kovacic and Wiggins. The effect caused by the parameters in the perturbed system are considered while computing the Melnikov fouction, and different phase portraits are obtained.At last, some meaningful results are summarized in the end of this thesis. Also some existing problems as well as the future work are pointed out.