The border collision normal form with stochastic switching surface

Glendinning, Paul (2012) The border collision normal form with stochastic switching surface. [MIMS Preprint]

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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: CICADA
Subjects: 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: 08 Aug 2012
Last Modified: 08 Nov 2017 18:18

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