摘要本文详细研究了具有限时滞van der Pol方程在经历 Hopf分枝时,小周期扰动对系统的影响,特别是讨论了扰动频率与Hopf分枝固有频率在共振(次调和共振,超调和共振)的情形。表明了在某些参数区域中,系统存在调和解分枝(次调和解分枝以及超调和解分枝),并且讨论了分枝解的稳定性以及时滞所起的作用。
8R H Plaut, J C Hsieh. Chaosin in mechanism with time delay under parametric and external[J]. Journal of Sound and Vibration, 1987,114 : 73-90.
9R M Laron, G N Bojadziev. Non-linear differential equations with damping and large time delay[J]. Journal of the Institute of Mathematics and its Applications, 1976,17 :3-35.
10R H Plaut, J C Hsieh. Non-linear structural vibrations involving a time deLay in damping[J]. Journal of Sound and Vibration, 1987,117(3):497-510.
