Reduction to invariant cones for non-smooth systems

T. Küpper and H.A. Hosham

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 81, issue 5, 980-995

Abstract: The reduction of smooth dynamical systems to lower dimensional center manifolds containing the essential bifurcation dynamics is a very useful approach both for theoretical investigations as well as for numerical computation. Since this approach relies on smoothness properties of the system and on the existence of a basic linearization the question arises if this approach can be carried over to non-smooth systems. Extending previous works we show that such a reduction is indeed possible by using an appropriate Poincaré map: the linearization will be replaced by a basic piecewise linear system; a fixed point of the Poincaré map generates an invariant cone which takes the role of the center manifold. The occurrence of nonlinear higher order terms will change this invariant “manifold” to a cone-like surface in Rn containing the essential dynamics of the original problem. In that way the bifurcation analysis can be reduced to the study of one-dimensional maps.

Keywords: Non-smooth dynamical systems; Invariant cones; Periodic orbits; Generalized Hopf bifurcation (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475410003101
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2011:i:5:p:980-995

DOI: 10.1016/j.matcom.2010.10.004

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().