The boundary focus-saddle bifurcation in planar piecewise linear systems. application to the analysis of memristor oscillators
type: Item
instance of: scholarly article
title: The boundary focus-saddle bifurcation in planar piecewise linear systems. application to the analysis of memristor oscillators
zbMATH Open document ID: 1402.34041
author: Enrique Ponce
author: Javier Ros
author: Elísabet Vela
published in: Nonlinear Analysis. Real World Applications
publication date: 2018-06-21T00:00:00Z
review text: This paper deals with bifurcation analysis of piecewise linear planar systems with a straight line \(\Sigma\), say the \(y\)-axis, separating the plane \(\mathbb{R}^2\) into two regions, \(S_L\) and \(S_R\). It requires the system to be refracting, i.e. the first component equation is continuous on \(\mathbb{R}^2\). So there are two possible cases: the second component equation is continuous or discontinuous on \(\Sigma\). In each of the cases, the system can be reduced to a canonical form to ease the analysis, and it shows that a boundary focus-saddle equilibrium bifurcation leads to one stable limit cycle surrounding the unstable focus under some condition, a homoclinic connection under another condition, and neither limit cycles nor homoclinic connections otherwise. Although there exist some results on piecewise continuous dynamical systems in the literature, this paper focuses on bifurcation analysis and applications of such systems.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 6892738
zbMATH Keywords: qualitative theory of planar ODEs
zbMATH Keywords: piecewise linear systems
zbMATH Keywords: limit cycles
zbMATH Keywords: bifurcation
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2018.03.011
OpenAlex ID: W2802161381
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DOI: 10.1016/J.NONRWA.2018.03.011
description: scientific article; zbMATH DE number 6892738