Limit cycles bifurcating from a perturbed quartic center

Bartomeu Coll, Jaume Llibre, Rafel Prohens

Research output: Contribution to journalArticleResearchpeer-review

23 Citations (Scopus)


We consider the quartic center ẋ=-yf(x,y),ẏ=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. © 2011 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)317-334
JournalChaos, Solitons and Fractals
Issue number4-5
Publication statusPublished - 1 May 2011


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