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Bifurcation analysis on a class of three-dimensional quadratic systems with twelve limit cycles

Author

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  • Guo, Laigang
  • Yu, Pei
  • Chen, Yufu

Abstract

This paper concerns bifurcation of limit cycles in a class of 3-dimensional quadratic systems with a special type of symmetry. Normal form theory is applied to prove that at least 12 limit cycles exist with 6–6 distribution in the vicinity of two singular points, yielding a new lower bound on the number of limit cycles in 3-dimensional quadratic systems. A set of center conditions and isochronous center conditions are obtained for such systems. Moreover, some simulations are performed to support the theoretical results.

Suggested Citation

  • Guo, Laigang & Yu, Pei & Chen, Yufu, 2019. "Bifurcation analysis on a class of three-dimensional quadratic systems with twelve limit cycles," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:39
    DOI: 10.1016/j.amc.2019.124577
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    Cited by:

    1. Li, Yongjun & Romanovski, Valery G., 2021. "Isochronous solutions of a 3-dim symmetric quadratic system," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    2. Ting Huang & Jieping Gu & Yuting Ouyang & Wentao Huang, 2023. "Bifurcation of Limit Cycles and Center in 3D Cubic Systems with Z 3 -Equivariant Symmetry," Mathematics, MDPI, vol. 11(11), pages 1-22, June.

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