非光滑微分方程周期解的渐近稳定性及其在vanderPol振子中的应用
Asymptotic stability of periodic solutions for nonsmooth differential equations with application to the nonsmooth van der Pol oscillator
摘要：
本文研究了一类具有小右端的Lipschitz系统周期解的存在唯一性和渐近稳定性。经典的假设在周期性的情况下，第二博戈柳博夫的定理意味着我们的。利用所得结果，我们构造了非光滑vanderPol振子的渐近稳定$2π$ --周期解的振幅与失谐量和微扰振幅的关系曲线.然后，我们将所得的共振曲线与Andronov和Witt首先构造的经典vanderPol振子的共振曲线进行了比较。
英文摘要：
In this paper we study the existence, uniqueness and asymptotic stability of the periodic solutions for a Lipschitz system with a small right hand side. Classical hypotheses in the periodic case of second Bogolyubov's theorem imply our ones. By means of the results established we construct the curves of dependence of the amplitude of asymptotically stable $2π$--periodic solutions of the nonsmooth van der Pol oscillator on the detuning parameter and the amplitude of the perturbation. After, we compare the resonance curves obtained, with the resonance curves of the classical van der Pol oscillator which were first constructed by Andronov and Witt.
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