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Noise induced resonance in bistable systems caused by delay feedback

Please always quote using this URN:urn:nbn:de:0296-matheon-3155
  • The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized stochastic differential equation with point delay, basic properties whereof we check. With a view to capturing the effective dynamics and, in particular, the resonance-like behaviour of the reference model we construct a simplified or reduced model, the two state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn can be used to characterize the phenomenon of noise-induced resonance. Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two state model and the reference model. The resonance characteristic developed for the reduced model can thus be applied to the original model.

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Metadaten
Author:Peter Imkeller, Markus Fischer
URN:urn:nbn:de:0296-matheon-3155
Referee:Anton Bovier
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/08/01
Release Date:2005/12/21
Tag:
Institute:Humboldt-Universität zu Berlin
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Kxx Functional-differential and differential-difference equations [See also 37-XX] / 34K11 Oscillation theory
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Kxx Functional-differential and differential-difference equations [See also 37-XX] / 34K13 Periodic solutions
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Kxx Functional-differential and differential-difference equations [See also 37-XX] / 34K18 Bifurcation theory
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Kxx Functional-differential and differential-difference equations [See also 37-XX] / 34K50 Stochastic functional-differential equations [See also , 60Hxx]
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G10 Stationary processes
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G17 Sample path properties
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05]
Preprint Number:302
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