在受迫Van der Pol振动系统的近似解的基础上,获得驱动系统的虚拟轨线.将虚拟轨线代入驱动－响应振动系统的近似误差方程,再用多尺度法求得同步时间关于反馈增益的分析表达式,并且将数值与分析结果进行比较表明：用该方法求得的同步时间与反馈增益的关系和数值模拟结果相当一致.这方法也适用于研究自激Van der Pol振动系统.
The virtual trajectories were obtained based on the approximate solution of the forced Van der Pol equation . By substituting the virtual trajectories into the approximate error system between the master and the response systems,we derived the relation between synchronization time and feedback gain by the multiple scale method. A fairly good agreement was obtained between the analytical and numerical results. The method is also valid for the selfsustained Van der Pol oscillator.
马米花,蔡建平. Van der Pol振动系统同步时间与反馈增益的关系[J].动力学与控制学报,2007,5(2):125~131; Ma Mihua, Cai Jianping. Relation between synchronization time and feedback gain of Van der Pol oscillator[J]. Journal of Dynamics and Control,2007,5(2):125-131.
