Mendler, Marc ; Falk, Johannes ; Drossel, Barbara (2019)
Analysis of stochastic bifurcations with phase portraits.
In: PLOS ONE, 2018, 13 (4)
Artikel, Zweitveröffentlichung, Verlagsversion
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Kurzbeschreibung (Abstract)
We propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective field correspond to maxima and minima of the stationary probability distribution if the probability current vanishes at these points. Stochastic phase portraits, which are vector plots of the convective field, therefore indicate the extrema of the stationary distribution and can be used to identify stochastic bifurcations that change the number and stability of these extrema. We show that limit cycles in stochastic phase portraits can indicate ridges of the probability distribution, and we identify a novel type of stochastic bifurcation, where the probability maximum moves to the edge of the system through a gap between the two nullclines of the convective field.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2019 |
| Autor(en): | Mendler, Marc ; Falk, Johannes ; Drossel, Barbara |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Analysis of stochastic bifurcations with phase portraits |
| Sprache: | Englisch |
| Publikationsjahr: | 2019 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | 2018 |
| Verlag: | PLOS |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | PLOS ONE |
| Jahrgang/Volume einer Zeitschrift: | 13 |
| (Heft-)Nummer: | 4 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/8642 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung aus gefördertem Golden Open Access |
| Kurzbeschreibung (Abstract): | We propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective field correspond to maxima and minima of the stationary probability distribution if the probability current vanishes at these points. Stochastic phase portraits, which are vector plots of the convective field, therefore indicate the extrema of the stationary distribution and can be used to identify stochastic bifurcations that change the number and stability of these extrema. We show that limit cycles in stochastic phase portraits can indicate ridges of the probability distribution, and we identify a novel type of stochastic bifurcation, where the probability maximum moves to the edge of the system through a gap between the two nullclines of the convective field. |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-86429 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 530 Physik |
| Fachbereich(e)/-gebiet(e): | 05 Fachbereich Physik 05 Fachbereich Physik > Institut für Festkörperphysik (2021 umbenannt in Institut für Physik Kondensierter Materie (IPKM)) |
| Hinterlegungsdatum: | 17 Apr 2019 14:26 |
| Letzte Änderung: | 20 Okt 2023 09:05 |
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- Analysis of stochastic bifurcations with phase portraits. (deposited 17 Apr 2019 14:26) [Gegenwärtig angezeigt]
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