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|Title:||On reducible nonlinear time - Delayed stochastic systems: Fluctuation-dissipation relations, transitions to bistability, and secondary transitions to non-stationarity|
T. D. Frank
I. M. Tang
Westfalische Wilhelms-Universitat Munster
|Keywords:||Mathematics;Physics and Astronomy|
|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.|
|Appears in Collections:||Scopus 2001-2005|
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