Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center

Junmin Yang and Pei Yu

Applied Mathematics and Computation, 2017, vol. 298, issue C, 141-152

Abstract: In this paper, we study bifurcation of limit cycles in planar cubic near-Hamiltonian systems with a nilpotent center. We use normal form theory to compute the generalized Lyapunov constants and show that there exist at least 9 limit cycles around the nilpotent center. This is a new lower bound on the number of limit cycles in planar cubic near-Hamiltonian systems with a nilpotent center.

Keywords: Near-Hamiltonian system; Nilpotent center; Hopf bifurcation; Limit cycle; Normal form; Generalized Lyapunov constant (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:298:y:2017:i:c:p:141-152

DOI: 10.1016/j.amc.2016.11.021

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