应用数学和力学2013，Vol.34Issue(7)：764-770,7.DOI:10.3879/j.issn.1000-0887.2013.07.012
具有时滞耦合的n个van der Pol振子弱共振双Hopf分岔
Weak Resonant Double Hopf Bifurcation of n van der Pol Oscillators With Delay Coupling
摘要
Abstract
Weak resonant double Hopf bifurcation of n van der Pol oscillators with delay coupiing was investigated.With an extended method of multiple scales,the complex amplitude equations were obtained.With the complex amplitudes expressed in a polar form,the complex amplitude equations were reduced to a two dimensional real amplitude system.The equilibria and their stability of the real amplitud equations were studied,and the dynamics around 2 ∶ 5resonant point unfolded and classified.Some interesting phenomena are found,such as amplitude death,periodic solution and bistability,etc.Validity of the analytical results is proved by their consistency with numerical simulations.关键词
双Hopf分岔/共振/van der Pol振子/多尺度方法Key words
double Hopf bifurcation/ resonance/ van der Pol oscillator/ method of multiple scales分类
数理科学引用本文复制引用
王万永,陈丽娟..具有时滞耦合的n个van der Pol振子弱共振双Hopf分岔[J].应用数学和力学,2013,34(7):764-770,7.基金项目
本文工作受到河南工程学院博士基金项目(D2012021)的资助,特此感谢. （D2012021）
