Bifurcation of limit cycles for a family of perturbed Kukles differential systems
type: Item
instance of: scholarly article
title: Bifurcation of limit cycles for a family of perturbed Kukles differential systems
zbMATH Open document ID: 1400.34046
author: Salomón Rebollo-Perdomo
author: Claudio Vidal
published in: Discrete and Continuous Dynamical Systems
publication date: 2018-08-16T00:00:00Z
review text: In this paper, the authors consider an integrable non-Hamiltonian system, which belongs to the quadratic Kukles differential systems having a center surrounded by a bounded period annulus. They study polynomial perturbations of such a Kukles system inside the Kukles family and apply averaging theory to study the limit cycles that bifurcate from the period annulus and from the center of the unperturbed system. First, it is shown that the periodic orbits of the period annulus can be parametrized explicitly through the Lambert function. Then, it is proved that at most one limit cycle bifurcates from the period annulus, under quadratic perturbations. Moreover, conditions are given for the non-existence, existence, and stability of the bifurcated limit cycle. Finally, by using averaging theory of seventh order, it is proved that there are cubic systems, close to the unperturbed system, with one and two small limit cycles.
reviewed by: Valery A. Gaiko
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 6919414
zbMATH Keywords: Kukles system
zbMATH Keywords: quadratic system
zbMATH Keywords: averaging theory
zbMATH Keywords: periodic orbit
zbMATH Keywords: limit cycle
MaRDI profile type: Publication
full work available at URL: dcds.2018182
OpenAlex ID: W2807581370
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Wikidata QID: Q129691326
DOI: 10.3934/DCDS.2018182
description: scientific article; zbMATH DE number 6919414