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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.

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  • Huanhuan Tian & Maoan Han, 2014. "Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-14, July.
    • Handle: RePEc:hin:jnlaaa:819798
    DOI: 10.1155/2014/819798
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    Cited by:

    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.

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