Publication:
On reducible nonlinear time - Delayed stochastic systems: Fluctuation-dissipation relations, transitions to bistability, and secondary transitions to non-stationarity

Issued Date

2005-12-25

Resource Type

Article

ISSN

03054470

DOI

10.1088/0305-4470/38/47/002

Other identifier(s)

2-s2.0-27844606876

Rights

Mahidol University

Rights Holder(s)

SCOPUS

Bibliographic Citation

Journal of Physics A: Mathematical and General. Vol.38, No.47 (2005), 10069-10083

Suggested Citation

K. Patanarapeelert, T. D. Frank, R. Friedrich, I. M. Tang On reducible nonlinear time - Delayed stochastic systems: Fluctuation-dissipation relations, transitions to bistability, and secondary transitions to non-stationarity. Journal of Physics A: Mathematical and General. Vol.38, No.47 (2005), 10069-10083. doi:10.1088/0305-4470/38/47/002 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/16640

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Title

On reducible nonlinear time - Delayed stochastic systems: Fluctuation-dissipation relations, transitions to bistability, and secondary transitions to non-stationarity

Author(s)

K. Patanarapeelert
 T. D. Frank
 R. Friedrich
 I. M. Tang

Other Contributor(s)

Mahidol University
 Westfalische Wilhelms-Universitat Munster

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.

Keyword(s)

Mathematics
 Physics and Astronomy

Availability

URI

https://repository.li.mahidol.ac.th/handle/123456789/16640

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Scopus 2001-2005