摘要
研究了具有时滞耦合的n个van der Pol振子系统中发生的弱共振双Hopf分岔.应用改进的多尺度方法,得到了2∶5共振的复振幅方程.通过将复振幅设为极坐标形式,将复振幅方程转化为一个二维的实振幅系统.通过研究实振幅方程的平衡点及其稳定性,对系统在2∶5共振点附近的动力学行为进行了开折和分类.得到了一些有趣的动力学现象,如振幅死区、周期解和双稳态解等,相应的数值模拟验证了理论结果的正确性.
Weak resonant double Hopf bifurcation of n van der Pol oscillators with delay cou- pling 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 ： 5 resonant point unfolded and classified. Some interesting phenomena are found, such as ampli- tude death, periodic solution and bistability, etc. Validity of the analytical results is proved by their consistency with numerical simulations.
出处
《应用数学和力学》
CSCD
北大核心
2013年第7期764-770,共7页
Applied Mathematics and Mechanics
基金
河南工程学院博士基金项目(D2012021)的资助
