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Isochronous solutions of a 3-dim symmetric quadratic system

Author

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  • Li, Yongjun
  • Romanovski, Valery G.

Abstract

In a family of real quadratic three dimensional systems symmetric with respect to a plane we look for subfamilies having center manifolds filled with isochronous periodic orbits. Eleven such subfamilies are detected and it is shown that for ten of them there are Darboux type substitutions transforming the subfamilies to systems which are linear on center manifolds. We also give an example of a 3-dim quadratic system with a compact isochronous periodic annulus.

Suggested Citation

  • Li, Yongjun & Romanovski, Valery G., 2021. "Isochronous solutions of a 3-dim symmetric quadratic system," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    • Handle: RePEc:eee:apmaco:v:405:y:2021:i:c:s0096300321003404
    DOI: 10.1016/j.amc.2021.126250
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    References listed on IDEAS

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    1. 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.
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