Bifurcation of limit cycles from a cubic reversible isochrone
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908264389672960 |
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| author | Yang, Jihua Zhang, Qipeng |
| author_facet | Yang, Jihua Zhang, Qipeng |
| contents | This paper is devoted to study the limit cycle problem of a cubic reversible system with an isochronous center, when it is perturbed inside a class of polynomials. An upper bound of the number of limit cycles is obtained using the Abelian integral. The algebraic structure of the Abelian integral is acquired thanks to some iterative formulas, which differs in many aspects from other methods. Some numerical simulations verify the existence of limit cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bifurcation of limit cycles from a cubic reversible isochrone Yang, Jihua Zhang, Qipeng Dynamical Systems This paper is devoted to study the limit cycle problem of a cubic reversible system with an isochronous center, when it is perturbed inside a class of polynomials. An upper bound of the number of limit cycles is obtained using the Abelian integral. The algebraic structure of the Abelian integral is acquired thanks to some iterative formulas, which differs in many aspects from other methods. Some numerical simulations verify the existence of limit cycles. |
| title | Bifurcation of limit cycles from a cubic reversible isochrone |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2503.09004 |