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Weiss, D., Kuepper, T. and Hosham, H. A. (2012). Invariant manifolds for nonsmooth systems. Physica D, 241 (22). S. 1895 - 1903. AMSTERDAM: ELSEVIER. ISSN 1872-8022

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Abstract

For piecewise smooth systems we describe mechanisms to obtain a similar reduction to a lower dimensional system as has been achieved for smooth systems via the center manifold approach. It turns out that for nonsmooth systems there are invariant quantities as well which can be used for a bifurcation analysis but the form of the quantities is more complicated. The approximation by piecewise linear systems (PWLS) provides a useful concept. In the case of PWLS, the invariant sets are given as invariant cones. For nonlinear perturbations of PWLS the invariant sets are deformations of those cones. The generation of invariant manifolds and a bifurcation analysis establishing periodic orbits are demonstrated; also an example for which multiple cones exist is provided. (C) 2011 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Weiss, D. UNSPECIFIED UNSPECIFIED UNSPECIFIED Kuepper, T. UNSPECIFIED UNSPECIFIED UNSPECIFIED Hosham, H. A. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-478893
DOI:	10.1016/j.physd.2011.07.012
Journal or Publication Title:	Physica D
Volume:	241
Number:	22
Page Range:	S. 1895 - 1903
Date:	2012
Publisher:	ELSEVIER
Place of Publication:	AMSTERDAM
ISSN:	1872-8022
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language GENERALIZED HOPF-BIFURCATION; PIECEWISE-LINEAR SYSTEMS; LIMIT-CYCLE BIFURCATION; CONES Multiple languages Mathematics, Applied; Physics, Fluids & Plasmas; Physics, Multidisciplinary; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47889