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Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle

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  • Huanhuan Tian
  • Maoan Han

Abstract

We study the expansions of the first order Melnikov functions for general near‐Hamiltonian systems near a compound loop with a cusp and a nilpotent saddle. We also obtain formulas for the first coefficients appearing in the expansions and then establish a bifurcation theorem on the number of limit cycles. As an application example, we give a lower bound of the maximal number of limit cycles for a polynomial system of Liénard type.

Suggested Citation

  • Huanhuan Tian & Maoan Han, 2014. "Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:819798
    DOI: 10.1155/2014/819798
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    References listed on IDEAS

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    1. Li, Jiao & Zhang, Tonghua & Han, Maoan, 2014. "Bifurcation of limit cycles from a heteroclinic loop with two cusps," Chaos, Solitons & Fractals, Elsevier, vol. 62, pages 44-54.
    2. Wang, Jihua, 2012. "Estimate of the number of zeros of Abelian integrals for a perturbation of hyperelliptic Hamiltonian system with nilpotent center," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1140-1146.
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