Bifurcation and Chaos Control of Van der pol System with Delay

摘要：

The dynamic characteristics of the Van der pol system with delay are investigated in this paper. By substituting variables, the characteristic equations are obtained. The stability of trivial equilibrium is discussed by analyzing distribution of the roots of the characteristic equations. If the system is instable on the equilibrium points, the roots of the characteristic equations should meet the equation Re (λ)=0, from which, the result of ω is got and the critical values of delay is found. It is found that Hopf bifurcation occurs from trivial equilibrium when the delay passes through critical values, then the critical values and their relations with system parameters are obtained. By adding delays to change the motion of the forced vibration of Van der pol system, and by numerical simulation, we got the time-delay system’s bifurcation diagram.

关键词： Van der pol Time delay Stability Bifurcation

作者: REN Chuan-bo ZHAO Zhen LIU Lin

作者单位: School of Traffic and Vehicle Engineering, Shandong University of Technology, Zibo255049, China

会议类型: 国际会议

会议名称: 2011 China Control and Decision Conference(2011中国控制与决策会议 CCDC)

会议地点: 四川绵阳

会议语种:英文

页码: 957-963

在线出版日期: 2011-05-23（万方平台首次上网日期，不代表论文的发表时间）