Academic Journal
On reducible nonlinear time-delayed stochastic systems: fluctuation–dissipation relations, transitions to bistability, and secondary transitions to non-stationarity: On reducible nonlinear time-delayed stochastic systems: fluctuation-dissipation relations, transitions to bistability, and secondary transitions to non-stationary
| Title: | On reducible nonlinear time-delayed stochastic systems: fluctuation–dissipation relations, transitions to bistability, and secondary transitions to non-stationarity: On reducible nonlinear time-delayed stochastic systems: fluctuation-dissipation relations, transitions to bistability, and secondary transitions to non-stationary |
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| Authors: | K. Patanarapeelert, R Friedrich, Till D. Frank, I-Ming Tang |
| Source: | Journal of Physics A: Mathematical and General. 38:10069-10083 |
| Publisher Information: | IOP Publishing, 2005. |
| Publication Year: | 2005 |
| Subject Terms: | numerical solution, Stochastic methods applied to problems in equilibrium statistical mechanics, fluctuation-dissipation thoerem, 0103 physical sciences, Fokker-Planck equations, Itô equations, 01 natural sciences |
| Description: | Summary: 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 \(1-x^2\) noise amplitude. |
| Document Type: | Article |
| File Description: | application/xml |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/38/47/002 |
| Access URL: | https://iopscience.iop.org/article/10.1088/0305-4470/38/47/002 https://iopscience.iop.org/article/10.1088/0305-4470/38/47/002/pdf http://iopscience.iop.org/article/10.1088/0305-4470/38/47/002/pdf http://ui.adsabs.harvard.edu/abs/2005JPhA...3810069P/abstract |
| Accession Number: | edsair.doi.dedup.....b3c73806443a16f86549f036739d6e9f |
| Database: | OpenAIRE |
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