具有限时滞Liénard方程的周期扰动Hopf分支

Periodically Perturbed Hopf Bifurcation of Liénard Equation with Limited Time Delay

详细研究了具有限时滞Liénard方程在经历Hopf分支时,小周期扰动对系统的影响,主要讨论了扰动频率与Hopf分支固有频率在共振、次调和共振、超调和共振和超次调和共振的情形,结果表明:在某些参数区域内,系统存在调和解分支、次调和解分支、超调和解分支和超次调和解分支,并且讨论了分支解的稳定性.

In this paper,periodically perturbed Hopf bifurcation to Liénard equation with limited time delay is studied in detail.That is,the influence of small periodic perturbations on system exhibiting Hopf bifurcation is studied.In particular,the excitation frequency and the critical natural frequency of Hopf bifurcation in the case of harmonic resonance,subharmonic resonance,ultraharmonic resonance and ultrasubharmonic is discussed.It is shown that in some parameter regions the systems exhibit harmonic solution b...