Border collision bifurcations, snap-back repellers and chaos

Glendinning, Paul and Wong, Chi Hong (2008) Border collision bifurcations, snap-back repellers and chaos. [MIMS Preprint]

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Abstract

The normal form for codimension one border collision bifurcations of fixed points of discrete time piecewise smooth dynamical systems is considered in the unstable case. We show that in appropriate parameter regions there is a snap-back repeller immediately after the bifurcation, and hence that the bifurcation creates chaos. Although the chaotic solutions are repellers they may explain observations, and this is illustrated through an example.

Item Type: MIMS Preprint
Uncontrolled Keywords: CICADA
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 39 Difference and functional equations
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems
Depositing User: Professor Paul Glendinning
Date Deposited: 27 Feb 2009
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1175

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