Hopf bifurcation from infinity for planar control systems
type: Item
instance of: scholarly article
title: Hopf bifurcation from infinity for planar control systems
zbMATH Open document ID: 0883.34043
DOI: 10.5565/PUBLMAT_41197_11
author: Jaume Llibre
author: Enrique Ponce
published in: Publicacions Matemàtiques
publication date: 1998-02-23T00:00:00Z
full work available at URL: https://eudml.org/doc/41281
review text: Symmetric, piecewise linear two-dimensional systems are shown to exhibit Hopf bifurcation from infinity at certain parameter values. After some linear coordinate transformations, yielding a simpler normal form for the piecewise linear system, a coordinate inversion is applied which maps infinity to the origin. Using polar coordinates the leading expansion of a one-dimensional Poincaré map is computed in a small neighborhood of the origin, which shows the transcritical bifurcation of a nontrivial fixed point from the origin, corresponding to a large periodic solution in the original system. Due to the nonsmooth system the Poincaré map must be calculated in pieces.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 1057641
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: inversion
zbMATH Keywords: piecewise linear system
zbMATH Keywords: Poincaré map
reviewed by: Alois Steindl
MaRDI profile type: Publication
OpenAlex ID: W4211263440
description: scientific article; zbMATH DE number 1057641