The third order melnikov function of a cubic integrable system under quadratic perturbations

R. Asheghi and A. Nabavi

Chaos, Solitons & Fractals, 2020, vol. 139, issue C

Abstract: In this work, we consider a cubic integrable system under quadratic perturbations. We then study the limit cycles of the perturbed system by using Melnikov functions up to order three. We prove that the sharp upper bound of the number of limit cycles lies between six and seven. Also, we give an example that shows six limit cycles.

Keywords: Melnikov functions; Integrable system; Quadratic perturbations; Limit cycles; Reversible (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920306871

DOI: 10.1016/j.chaos.2020.110291

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