Bifurcation analysis on a class of \(Z_{2}\)-equivariant cubic switching systems showing eighteen limit cycles
type: Item
instance of: scholarly article
title: Bifurcation analysis on a class of \(Z_{2}\)-equivariant cubic switching systems showing eighteen limit cycles
zbMATH Open document ID: 1410.34115
author: Y. Aharonov
published in: Journal of Differential Equations
publication date: 2018-12-03T00:00:00Z
review text: In this paper, the authors apply the method developed for computing the Lyapunov constants of planar switching systems associated with an elementary singular point to study bifurcations of limit cycles in a cubic switching system. A complete classification on the center conditions and 16 limit cycles are obtained around the two foci of this system. Further, with this method, the authors construct an example of a cubic switching system to show the existence of 18 small-amplitude limit cycles bifurcating from the centers. This is a new lower bound on the maximal number of small-amplitude limit cycles obtained in such cubic switching systems. Finally, a method to show the realization of the 18 limit cycles is presented.
reviewed by: Valery A. Gaiko
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A36
zbMATH DE Number: 6987658
zbMATH Keywords: switching system
zbMATH Keywords: \(Z_2\)-equivariant system
zbMATH Keywords: Lyapunov constant
zbMATH Keywords: center
zbMATH Keywords: limit cycle
MaRDI profile type: Publication
full work available at URL: j.jde.2018.07.071
OpenAlex ID: W2888494538
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Wikidata QID: Q129359515
DOI: 10.1016/J.JDE.2018.07.071
description: scientific article; zbMATH DE number 6987658