Limit cycles near a compound cycle in a near-Hamiltonian system with smooth perturbations

Junmin Yang and Maoan Han

Chaos, Solitons & Fractals, 2024, vol. 184, issue C

Abstract: In this paper, we give a simple relation between the coefficients appearing in the expansions of n+2 (n∈Z+,n≥2) Melnikov functions near a compound cycle C(n), which can be used to simplify some computations. We further give some conditions for a general near-Hamiltonian system to have limit cycles as many as possible near C(n). Based on this, for a quintic Hamiltonian system with a compound cycle C(2) we prove that it can produce at least 72(n−2)+12(1+(−1)n) limit cycles near C(2) under polynomial perturbation of degree n(n≥2).

Keywords: Limit cycle; Compound cycle; Melnikov function; Bifurcation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005150

DOI: 10.1016/j.chaos.2024.114963

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