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arXiv · 1412.1126

On periodic perturbations of asymmetric Duffing-Van-der-Pol equation

Albert D. Morozov·Olga S. Kostromina
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Abstract

Time-periodic perturbations of an asymmetric Duffing-Van-der-Pol equation close to an integrable equation with a homoclinic "figure-eight" of a saddle are considered. The behavior of solutions outside the neighborhood of "figure-eight" is studied analytically. The problem of limit cycles for an autonomous equation is solved and resonance zones for a nonautonomous equation are analyzed. The behavior of the separatrices of a fixed saddle point of the Poincare map in the small neighborhood of the unperturbed "figure-eight" is ascertained. The results obtained are illustrated by numerical computations.

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Albert D. Morozov, Olga S. Kostromina. 2014-12-02. On periodic perturbations of asymmetric Duffing-Van-der-Pol equation. https://doi.org/10.1142/s0218127414500618

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