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Bi-center conditions and local bifurcation of critical periods in a switching Z2 equivariant cubic system

Author

Listed:
  • Chen, Ting
  • Huang, Lihong
  • Huang, Wentao
  • Li, Wenjie

Abstract

In this study, we consider bi-centers and local bifurcation of critical periods for a switching Z2 equivariant cubic system. We give the necessary and sufficient conditions for the system to have bi-centers at the symmetrical singular points ( ± 1, 0). We develop a method for computing the period constants near the center of switching systems and use this method to study bifurcation of critical periods for a switching system. We further find the existence of 10 local critical periods bifurcating from these bi-centers.

Suggested Citation

  • Chen, Ting & Huang, Lihong & Huang, Wentao & Li, Wenjie, 2017. "Bi-center conditions and local bifurcation of critical periods in a switching Z2 equivariant cubic system," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 157-168.
    • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:157-168
    DOI: 10.1016/j.chaos.2017.10.024
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    References listed on IDEAS

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    1. Wang, Yanqin & Han, Maoan & Constantinescu, Dana, 2016. "On the limit cycles of perturbed discontinuous planar systems with 4 switching lines," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 158-177.
    2. Li, Feng & Liu, Yuanyuan, 2016. "Limit cycles in a class of switching system with a degenerate singular point," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 86-90.
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    Cited by:

    1. Liu, Yuanyuan & He, Dongping & Huang, Wentao, 2023. "Weak centers and local criticality on planar Z2-symmetric cubic differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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    More about this item

    Keywords

    Switching system; Z2 equivariant system; Lyapunov constant; Bi-center; Bifurcation of critical periods;
    All these keywords.

    JEL classification:

    • Z2 - Other Special Topics - - Sports Economics

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