国家自然科学基金资助项目(10372116, 50135030)
以van der Pol系统为例，揭示了多尺度法在求解非线性系统三次以上近似解时似乎存在的二义性问题.通过将多尺度法的结果与KBM法所得结果进行比较，指出了如何利用多尺度法求解非线性系统三次以上近似解的正确步骤.
This paper reveals the seeming ambiguity problem of the method of multiple scales in solving the third or higher order approximate solutions of nonlinear systems through an example of the famous van der Pol equation. By comparing the results obtained by the method of multiple scales with that of the KBM method, the paper indicates a proper way about how to apply the method of multiple scales to solving the third or higher order approximate solutions of nonlinear systems.
王怀磊,胡海岩.关于多尺度法的一个注记[J].动力学与控制学报,2004,2(3):10~13; Wang Huailei, Hu Haiyan. A note on the method of multiple scales[J]. Journal of Dynamics and Control,2004,2(3):10-13.
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