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对含有时滞位移和时滞速度的vanderPol方程进行了研究,着重研究了时滞参数对vanderPol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.
The vanderPol equation with time-lag displacement and delay velocity is studied, and the influence of delay parameters on the van der Pol equation limit-cycle amplitude is studied emphatically.Firstly, by using perturbation method, the limit-ring amplitude and delay parameters The influence of delay parameters on the amplitude is analyzed, and the control of the amplitude under the condition of not changing the vibration frequency is emphatically discussed.Finally, the numerical calculation method is used to verify the theoretical calculation results. The results show that the numerical results are in good agreement with The theoretical results are quite consistent.