Limit cycles bifurcating from the quasi-homogeneous polynomial centers of weight-degree 2 under non-smooth perturbations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912305723211776 |
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| author | Sui, Shiyou Zhang, Yongkang Li, Baoyi |
| author_facet | Sui, Shiyou Zhang, Yongkang Li, Baoyi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit cycles bifurcating from the quasi-homogeneous polynomial centers of weight-degree 2 under non-smooth perturbations Sui, Shiyou Zhang, Yongkang Li, Baoyi Dynamical Systems 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. |
| title | Limit cycles bifurcating from the quasi-homogeneous polynomial centers of weight-degree 2 under non-smooth perturbations |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.01661 |