摘要
对含有两个时滞参数、受简谐激励作用下的van der Pol-Duffing方程进行了研究,着重研究了时滞参数对该类参数激励系统的主共振的分岔响应控制.首先采用摄动法从理论上推导出时滞动力系统的分岔响应方程,用奇异性理论得到了退化余维一分岔和余维二分岔的条件,以及Hopf分岔的存在性及发生该分岔的条件,最后用数值模拟的方法研究了时滞参数对系统分岔响应的影响.研究结果表明,适当选取时滞参数,不仅可以改变分岔响应曲线的拓扑形态,还可以改变分岔点的位置.
A forced system with two time-delays, including van der Pol-Duffing types, is studied. The aim is to study the primary parametrical resonance bifurcation of this system. Perturbation method is used to obtain the bifurcation equation with time-delays. Based on the bifurcation equation, co-dimension one, co-dimension two and Hope bifurcation are discussed, and the effect of time-delays on the steady state response is analyzed by numerical methods. It is indicated that the primary resonance bifurcation can be well controlled by time-delays feedback.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2006年第2期617-621,共5页
Acta Physica Sinica
基金
国家自然科学基金(批准号:10472029)资助的课题.~~
关键词
摄动法
分岔控制
时滞动力系统
perturbation method, bifurcation control, dynamics of nonlinear systems involving time delays
