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

Huanhuan Tian and Maoan Han

Abstract and Applied Analysis, 2014, vol. 2014, 1-14

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:819798

DOI: 10.1155/2014/819798

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