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Limit cycles for perturbing a piecewise linear Hamiltonian system with one or two saddles

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  • Liu, Yuanyuan
  • Xiong, Yanqin

Abstract

We study bifurcations of limit cycles arising after perturbations of linear piecewise Hamiltonian systems. In this paper we find bounds for the numbers of limit cycles for several families of which phase portraits were classified in Xiong and Han (2013) [14].

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:66:y:2014:i:c:p:86-95
    DOI: 10.1016/j.chaos.2014.05.010
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    References listed on IDEAS

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    1. Liang, Feng & Han, Maoan, 2012. "Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 454-464.
    2. Yanqin Xiong & Maoan Han, 2013. "Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-19, February.
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    Cited by:

    1. Liang, Feng & Romanovski, Valery G. & Zhang, Daoxiang, 2018. "Limit cycles in small perturbations of a planar piecewise linear Hamiltonian system with a non-regular separation line," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 18-34.
    2. Zhang, Huihui & Xiong, Yanqin, 2023. "Hopf bifurcations by perturbing a class of reversible quadratic systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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