On the number of limit cycles bifurcated from some Hamiltonian systems with a non-elementary heteroclinic loop

Pegah Moghimi, Rasoul Asheghi and Rasool Kazemi

Chaos, Solitons & Fractals, 2018, vol. 113, issue C, 345-355

Abstract: In this paper, we study the bifurcation of limit cycles in two special near-Hamiltonian polynomial planer systems which their corresponding Hamiltonian systems have a heteroclinic loop connecting a hyperbolic saddle and a cusp of order two. In these systems, we will compute the asymptotic expansions of corresponding first order Melnikov functions near the loop and the center to analyze the number of limit cycles. Moreover, in the first system, by using the Chebychev criterion, we study the Poincaré bifurcation.

Keywords: Limit cycle; Bifurcation; Hamiltonian system; Melnikov function; Asymptotic expansion (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:113:y:2018:i:c:p:345-355

DOI: 10.1016/j.chaos.2018.05.023

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