摘要
研究了具有限时滞Liénard方程在经历Hopf分支时小周期扰动对系统的影响,特别是讨论了扰动频率与Hopf分支周期解的固有频率在二阶次调和共振的情形.给出了系统的次调和解分支及其稳定性,并且讨论了相应的平均系统Hopf分支.
In this paper, the influence of small periodic perturbations on Liénard equation with limited delay exhibiting Hopf bifurcation is studied. In particular, the case where the excitation frequency is close to twice the critical natural frequency of Hopf bifurcation is discussed. The result of subharmonic solution bifurcation along with its stability is obtained. And Hopf bifurcation of the averaged system is studied.
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2010年第3期361-364,368,共5页
Journal of Central China Normal University：Natural Sciences
基金
国家自然科学基金项目(10671081)
关键词
周期扰动
HOPF分支
次调和解分支
平均系统
稳定性
periodic perturbations
Hopf bifurcation
subharmonic solution bifurcation
averaged system
stability
