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Global Phase Portraits of Separable Polynomial Rigid Systems with a Center

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Abstract

In this paper, we study dynamics of a class of separable polynomial rigid systems and classify global phase portraits under certain conditions. Some complicated and interesting dynamical behaviors are demonstrated.

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Acknowledgements

The authors are very grateful to the anonymous referees for the valuable comments that greatly improve the presentation and quality of this article.

The first and third authors are supported by National Natural Science Foundation of China (Nos. 12322109 and 12171485) and Science and Technology Innovation Program of Hunan Province (No. 2023RC3040). The second author is partially supported by NSF-DMS 2316952. The third author is partially supported by Hunan Provincial Innovation Foundation for Postgraduate (No. CX20240165).

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Authors and Affiliations

  1. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, 410083, Hunan, China

    Hebai Chen & Rui Zhang

  2. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX, 78539, USA

    Zhaosheng Feng

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  1. Hebai Chen
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  2. Zhaosheng Feng
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Correspondence to Zhaosheng Feng.

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Communicated by Luis Garcia-Naranjo.

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Chen, H., Feng, Z. & Zhang, R. Global Phase Portraits of Separable Polynomial Rigid Systems with a Center. J Nonlinear Sci 35, 6 (2025). https://doi.org/10.1007/s00332-024-10104-9

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