Boundary intersection crossing bifurcation in the presence of sliding
type: Item
instance of: scholarly article
title: Boundary intersection crossing bifurcation in the presence of sliding
zbMATH Open document ID: 1166.37020
author: A. Colombo
published in: Physica D
publication date: 2009-02-10T00:00:00Z
review text: The paper deals with a class of discontinuity induced bifurcations that result from interactions between periodic orbits and the intersection of two or more discontinuity boundaries (between periodic orbits and corners of discontinuity boundaries). The wide variety of qualitatively different configurations makes the analysis of such bifurcations very difficult. The author starts with some observations on uniqueness of solutions in the presence of boundary intersections. Then the concepts of zero-time discontinuity mapping and Poincaré discontinuity mapping are explained, and the discontinuity mapping is derived in a quite general setting for the case of two intersecting boundaries in the presence of sliding. The results are applied to the analysis of a model of a buck converter. The ideas proposed in the paper can be implemented in bifurcation analysis software for the characterization of discontinuity induced bifurcations and the detection of bifurcations of higher codimensions.
Mathematics Subject Classification ID: 37G25
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 37C27
zbMATH DE Number: 5506294
zbMATH Keywords: boundary intersection crossing bifurcation
zbMATH Keywords: periodic orbits
zbMATH Keywords: discontinuity mapping
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
full work available at URL: j.physd.2008.05.002
OpenAlex ID: W2165175255
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DOI: 10.1016/J.PHYSD.2008.05.002
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description: scientific article; zbMATH DE number 5506294