具有限时滞的扰动Van der pol方程的次调和分支

Subharmonic Bifurcation of Van der pol Equation with Limited Time Delay

详细研究了具有限时滞van der po l方程在经历Hop f分支时,小周期扰动对系统的影响,特别讨论了扰动频率与Hop f分支固有频率在次调和共振的情形,表明了在某些参数区域内,系统存在次调和分支,并且讨论了其分支解的稳定性.

In this paper periodically perturbed Hopf bifurcation to Van der pol 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 ease of subharmonie resonance is discussed . It is shown that in some parameter regions the systems exhibit subharmonie solution bifurcation. Furthermore, the stability of bifurcation periodic solutions is discussed.