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Hopf bifurcations by perturbing a class of reversible quadratic systems

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  • Zhang, Huihui
  • Xiong, Yanqin

Abstract

This paper first investigates the dynamical behavior of a class of reversible quadratic systems, providing all possible phase portraits on the plane. Then, we use generalized Melnikov function method to study the Hopf bifurcation of reversible quadratic systems under the perturbation of piecewise quadratic systems, finding 4 more limit cycles than the smooth case.

Suggested Citation

  • Zhang, Huihui & Xiong, Yanqin, 2023. "Hopf bifurcations by perturbing a class of reversible quadratic systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002102
    DOI: 10.1016/j.chaos.2023.113309
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    References listed on IDEAS

    as
    1. Liu, Yuanyuan & Xiong, Yanqin, 2014. "Limit cycles for perturbing a piecewise linear Hamiltonian system with one or two saddles," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 86-95.
    2. Xiong, Yanqin & Hu, Jianqiang, 2019. "A class of reversible quadratic systems with piecewise polynomial perturbations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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