Abstract: This paper provides a parallel algorithm to treat periodic orbit and period of second-order coupled Vanderpol oscillator with multi degree of freedom. By changing the time scale, the period of the system is drawn into the governing equation, and then solves an initial value problem through a multi-splitting waveform relaxation method which can transform a boundary value problems into initial value problem. At the same time, in order to calculate the system period, it designs a period iteration algorithm. Finally, this paper gives some numerical simulation studies of the system in order to verify the analytic results.

Key words: limit cycle, Vanderpol oscillator, parallel algorithm, multi-splitting waveform relaxation methods

摘要： 提出了一种确定二阶多自由度Vanderpol振子周期轨道及周期的并行算法。通过改变系统的时间尺度，将系统周期转化为系统的变量，进而通过多分裂波形松弛法将边值问题转化为初值问题进行求解；同时为了计算系统周期，设计了周期迭代算法。最后通过数值示例进行仿真，进行了强有力的论证。

关键词: 极限环, Vanderpol振子, 并行算法, 多分裂波形松弛