Limit cycles of a perturbed cubic polynomial differential center

Adriana Buică and Jaume Llibre

Chaos, Solitons & Fractals, 2007, vol. 32, issue 3, 1059-1069

Abstract: In this paper we study the limit cycles of the system x˙=-y(x+a)(y+b)+εP(x,y), y˙=x(x+a)(y+b)+εQ(x,y) for ε sufficiently small, where a,b∈R⧹{0}, and P, Q are polynomials of degree n. We obtain that 3[(n−1)/2]+4 if a≠b and, respectively, 2[(n−1)/2]+2 if a=b, up to first order in ε, are upper bounds for the number of the limit cycles that bifurcate from the period annulus of the cubic center given by ε=0. Moreover, there are systems with at least 3[(n−1)/2]+2 limit cycles if a≠b and, respectively, 2[(n−1)/2]+1 if a=b.

Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007790501129X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:32:y:2007:i:3:p:1059-1069

DOI: 10.1016/j.chaos.2005.11.060

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().