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Analysis of stochastic bifurcations with phase portraits

Mendler, Marc and Falk, Johannes and Drossel, Barbara (2018):
Analysis of stochastic bifurcations with phase portraits.
In: PloS one, PloS, 13, (4), ISSN 1932-6203, DOI: 10.1371/journal.pone.0196126, [Online-Edition: https://doi.org/10.1371/journal.pone.0196126],
[Article]

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.

Item Type: Article
Erschienen: 2018
Creators: Mendler, Marc and Falk, Johannes and Drossel, Barbara
Title: Analysis of stochastic bifurcations with phase portraits
Language: English
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.

Journal or Publication Title: PloS one
Volume: 13
Number: 4
Publisher: PloS
Divisions: 05 Department of Physics
05 Department of Physics > Institute for condensed matter physics
05 Department of Physics > Institute for condensed matter physics > Statistische Physik und komplexe Systeme
Date Deposited: 13 Aug 2018 08:53
DOI: 10.1371/journal.pone.0196126
Official URL: https://doi.org/10.1371/journal.pone.0196126
URN: urn:nbn:de:tuda-tuprints-86429
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