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Title: On reducible nonlinear time - Delayed stochastic systems: Fluctuation-dissipation relations, transitions to bistability, and secondary transitions to non-stationarity
Authors: K. Patanarapeelert
T. D. Frank
R. Friedrich
I. M. Tang
Mahidol University
Westfalische Wilhelms-Universitat Munster
Keywords: Mathematics;Physics and Astronomy
Issue Date: 25-Dec-2005
Citation: Journal of Physics A: Mathematical and General. Vol.38, No.47 (2005), 10069-10083
Abstract: We show the conditions under which nonlinear time-delayed dynamical systems with multiplicative noise sources can be transformed into linear time-delayed systems with additive noise sources. We show that, for such reducible systems, analytical expressions for stationary distributions can be obtained. We demonstrate that fluctuation-dissipation relations of reducible systems become trivial and we show that reducible systems may exhibit delay- and noise-induced transitions to bistability and secondary transitions to non-stationarity. Our general findings are exemplified for three models: a Gompertz model, a Hongler model and a model involving a 1 - x2 noise amplitude. © 2005 IOP Publishing Ltd.
ISSN: 03054470
Appears in Collections:Scopus 2001-2005

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