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2014 Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle
Huanhuan Tian, Maoan Han
Abstr. Appl. Anal. 2014(SI66): 1-14 (2014). DOI: 10.1155/2014/819798

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. "Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle." Abstr. Appl. Anal. 2014 (SI66) 1 - 14, 2014. https://doi.org/10.1155/2014/819798

Information

Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07023141
MathSciNet: MR3240564
Digital Object Identifier: 10.1155/2014/819798

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI66 • 2014
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