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Analysis of stochastic bifurcations with phase portraits

Mendler, Marc ; Falk, Johannes ; Drossel, Barbara (2019)
Analysis of stochastic bifurcations with phase portraits.
In: PLOS ONE, 2018, 13 (4)
Artikel, Zweitveröffentlichung

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
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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.

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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