Limit cycles bifurcating from a perturbed quartic center

Bartomeu Coll, Jaume Llibre and Rafel Prohens

Chaos, Solitons & Fractals, 2011, vol. 44, issue 4, 317-334

Abstract: We consider the quartic center x˙=-yf(x,y),y˙=xf(x,y), with f(x,y)=(x+a) (y+b) (x+c) and abc≠0. Here we study the maximum number σ of limit cycles which can bifurcate from the periodic orbits of this quartic center when we perturb it inside the class of polynomial vector fields of degree n, using the averaging theory of first order. We prove that 4[(n−1)/2]+4⩽σ⩽5[(n−1)/2]+14, where [η] denotes the integer part function of η.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:44:y:2011:i:4:p:317-334

DOI: 10.1016/j.chaos.2011.02.009

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