EconStor >
Humboldt-Universität Berlin >
Sonderforschungsbereich 649: Ökonomisches Risiko, Humboldt-Universität Berlin >
SFB 649 Discussion Papers, HU Berlin >

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10419/25036
  
Title:A two state model for noise-induced resonance in bistable systems with delay PDF Logo
Authors:Fischer, Markus
Imkeller, Peter
Issue Date:2005
Series/Report no.:SFB 649 discussion paper 2005,017
Abstract: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 characteristics developed for the reduced model can thus be applied to the original model.
Subjects:stochastic differential equation
delay differential equation
stochastic resonance
effective dynamics
Markov chain
stationary process
stochastic synchronization
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

Files in This Item:
File Description SizeFormat
496021400.PDF985.75 kBAdobe PDF
No. of Downloads: Counter Stats
Download bibliographical data as: BibTeX
Share on:http://hdl.handle.net/10419/25036

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.