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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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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:819798
DOI: 10.1155/2014/819798
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