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2012.76: The border collision normal form with stochastic switching surface

2012.76: Paul Glendinning (2012) The border collision normal form with stochastic switching surface.

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Abstract

The deterministic border collision normal form describes the bifurcations of a discrete time dynamical system as a fixed point moves across the switching surface with changing parameter. If the position of the switching surface varies randomly, but within some bounded region, we give conditions which imply that the attractor close to the bifurcation point is the attractor of an Iterated Function System. The proof uses an equivalent metric to the Euclidean metric because the functions involved are never contractions in the Euclidean metric. If the conditions do not hold then a range of possibilities may be realized, including local instability, and some examples are investigated numerically.

Item Type:MIMS Preprint
Additional Information:

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Subjects:PACS 2003 > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems
MIMS number:2012.76
Deposited By:Professor Paul Glendinning
Deposited On:08 August 2012

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