Mendler, Marc ; Falk, Johannes ; Drossel, Barbara (2018)
Analysis of stochastic bifurcations with phase portraits.
In: PloS one, 13 (4)
doi: 10.1371/journal.pone.0196126
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
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: | 2018 |
| Autor(en): | Mendler, Marc ; Falk, Johannes ; Drossel, Barbara |
| Art des Eintrags: | Bibliographie |
| Titel: | Analysis of stochastic bifurcations with phase portraits |
| Sprache: | Englisch |
| Publikationsjahr: | 24 April 2018 |
| Verlag: | PloS |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | PloS one |
| Jahrgang/Volume einer Zeitschrift: | 13 |
| (Heft-)Nummer: | 4 |
| DOI: | 10.1371/journal.pone.0196126 |
| URL / URN: | https://doi.org/10.1371/journal.pone.0196126 |
| Zugehörige Links: | |
| 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. |
| 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)) 05 Fachbereich Physik > Institut für Festkörperphysik (2021 umbenannt in Institut für Physik Kondensierter Materie (IPKM)) > Statistische Physik und komplexe Systeme |
| Hinterlegungsdatum: | 13 Aug 2018 08:53 |
| Letzte Änderung: | 03 Jul 2024 02:30 |
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| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
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Analysis of stochastic bifurcations with phase portraits. (deposited 17 Apr 2019 14:26)
- Analysis of stochastic bifurcations with phase portraits. (deposited 13 Aug 2018 08:53) [Gegenwärtig angezeigt]
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