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Rigid polynomial differential systems with quartic homogeneous nonlinearities

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  • Li, Yingtao
  • Llibre, Jaume

Abstract

In this paper we classify the global phase portraits in the Poincaré disc of all rigid polynomial differential systems with quartic homogeneous nonlinearities. We show that these systems exhibit thirteen distinct topological phase portraits in the Poincaré disc, revealing some complex and interesting dynamical phenomena.

Suggested Citation

  • Li, Yingtao & Llibre, Jaume, 2025. "Rigid polynomial differential systems with quartic homogeneous nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925008173
    DOI: 10.1016/j.chaos.2025.116804
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    References listed on IDEAS

    as
    1. Llibre, Jaume & Valls, Claudia, 2024. "The phase portrait of all polynomial Liénard isochronous centers," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Jaume Llibre, 2024. "Rigid Polynomial Differential Systems with Homogeneous Nonlinearities," Mathematics, MDPI, vol. 12(18), pages 1-10, September.
    3. Freddy Dumortier & Jaume Llibre & Joan C. Artés, 2006. "Qualitative Theory of Planar Differential Systems," Springer Books, Springer, number 978-3-540-32902-2, October.
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