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Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System

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  • Yanqin Xiong
  • Maoan Han

Abstract

This paper concerns limit cycle bifurcations by perturbing a piecewise linear Hamiltonian system. We first obtain all phase portraits of the unperturbed system having at least one family of periodic orbits. By using the first‐order Melnikov function of the piecewise near‐Hamiltonian system, we investigate the maximal number of limit cycles that bifurcate from a global center up to first order of ε.

Suggested Citation

  • Yanqin Xiong & Maoan Han, 2013. "Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:575390
    DOI: 10.1155/2013/575390
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    References listed on IDEAS

    as
    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, 2012. "Hopf Bifurcation of Limit Cycles in Discontinuous Liénard Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-27, September.
    3. Yanqin Xiong & Maoan Han, 2012. "Hopf Bifurcation of Limit Cycles in Discontinuous Liénard Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Jing Tian, 2014. "On the Number of Limit Cycles of a Piecewise Quadratic Near‐Hamiltonian System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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