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arXiv · 1609.08048

On the number of limit cycles for a class of discontinuous quadratic differential systems

Xiuli Cen·Shimin Li·Yulin Zhao
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Abstract

The present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center $\dot{x}=-y+\frac{16}{3}x^{2}-\frac{4}{3}y^{2},\dot{y}=x+\frac{8}{3}xy$ by the averaging method of first order, when it is perturbed inside a class of discontinuous quadratic polynomial differential systems. The \emph{Chebyshev criterion} is used to show that this maximum number is 5 and can be realizable. The result and that in paper \cite{LC} completely answer the questions left in the paper \cite{LM}.

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Xiuli Cen, Shimin Li, Yulin Zhao. 2016-09-26. On the number of limit cycles for a class of discontinuous quadratic differential systems. https://arxiv.org/abs/1609.08048

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