Analysis and Controlling of Hopf Bifurcation for Chaotic Van Der Pol-Duffing System

Mathematical and Computational Applications

Cai, Ping¹ 

关键词: chaotic Van der Pol-Duffing system;    hopf bifurcation;    amplitude of limit cycle;    controller;   

DOI  :  10.3390/mca19030184

学科分类：计算数学

来源: mdpi

【 摘 要 】

Analysis and controlling of bifurcation for a class of chaotic Van der Pol- Duffing system with multiple unknown parameters are conducted. The stability of the equilibrium of the system is studied by using Routh-Hurwitz criterion, and the critical value of Hopf bifurcation is investigated. Based on the center manifold theory and normal form reduction, the stability index of bifurcation solution is given. Linear and nonlinear washout filter feedback controllers are designed respectively to control the bifurcation critical value and the amplitude of the limit cycle. Numerical simulation results are presented to illustrate analytical results found.

【 授权许可】

CC BY