Amplitude control of limit cycle in van der Pol system with time delays
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摘要:
对含有时滞位移和时滞速度的van der Pol方程进行了研究，着重研究了时滞参数对van der Pol方程极限环幅值的影响．首先采用摄动法从理论上推导出极限环幅值与时滞参数之间的关系，分析时滞参数对幅值大小的影响，并着重讨论了不改变振动频率情况下对幅值的控制．最后用数值计算的方法验证了理论计算结果，结果表明数值计算结果与理论结果相当吻合．
Abstract:
This paper studied the van der Pol equation with two time delays, particularly the amplitude control of limit cycle in van der Pol system with time delays. The perturbation method was used to obtain the relation equation between amplitude and timedelays. Based on the equation, the controlling of time delays to amplitude were discussed. Then numerical method was utilized to testify theoretic result.
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钱长照,彭献. van der Pol系统极限环幅值的时滞控制[J].动力学与控制学报,2005,3(2):25~28; Qian Changzhao, Peng Xian. Amplitude control of limit cycle in van der Pol system with time delays[J]. Journal of Dynamics and Control,2005,3(2):25-28.
