On reducible nonlinear time - Delayed stochastic systems: Fluctuation-dissipation relations, transitions to bistability, and secondary transitions to non-stationarity
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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://repository.li.mahidol.ac.th/handle/123456789/16640 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Mahidol University |
| 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 - x2 noise amplitude. © 2005 IOP Publishing Ltd. |
|---|