On the bifurcation of periodic orbits in discontinuous systems
type: Item
instance of: scholarly article
title: On the bifurcation of periodic orbits in discontinuous systems
zbMATH Open document ID: 1213.34018
author: Michal Fečkan
author: Michal Pospíšil
published in: Communications in Mathematical Analysis
publication date: 2010-05-12T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.cma/1270646496
review text: Bifurcation scenarios of periodic orbits in discontinuous systems are discussed; such systems are given by differential equations with discontinuity boundaries which divide the phase space into two (or more) parts. The authors first use a Poincaré function and a method of Melnikov type to give a sufficient condition for the persistence of a piecewise \(C^1\)-orbit. Sufficient conditions for bifurcations in planar discontinuous systems (a piecewise nonlinear and linear equation) are discussed in the last part of the paper.
reviewed by: Martin Rasmussen
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 5707205
zbMATH Keywords: periodic orbit
zbMATH Keywords: discontinuous system
zbMATH Keywords: bifurcation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5707205