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arXiv · 2504.01661

Limit cycles bifurcating from the quasi-homogeneous polynomial centers of weight-degree 2 under non-smooth perturbations

Shiyou Sui·Yongkang Zhang·Baoyi Li
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Abstract

We investigate the maximum number of limit cycles bifurcating from the period annulus of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic piecewise smooth polynomials. The family considered is the unique family of weight-homogeneous polynomial differential systems of weight-degree 2 with a center. When the switching line is $x=0$ or $y=0$, we obtain the sharp bounds of the number of limit cycles for the perturbed systems by using the first order averaging method. Our results indicate that non-smooth systems can have more limit cycles than smooth ones, and the switching lines play an important role in the dynamics of non-smooth systems.

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Shiyou Sui, Yongkang Zhang, Baoyi Li. 2025-04-02. Limit cycles bifurcating from the quasi-homogeneous polynomial centers of weight-degree 2 under non-smooth perturbations. https://arxiv.org/abs/2504.01661

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