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2008.114: Border collision bifurcations, snap-back repellers and chaos

2008.114: Paul Glendinning and Chi Hong Wong (2008) Border collision bifurcations, snap-back repellers and chaos.

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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 2000 > 39 Difference and functional equations
PACS 2003 > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems
MIMS number:2008.114
Deposited By:Professor Paul Glendinning
Deposited On:27 February 2009

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