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Analysis of stochastic bifurcations with phase portraits

Mendler, Marc ; Falk, Johannes ; Drossel, Barbara (2018):
Analysis of stochastic bifurcations with phase portraits.
In: PLOS ONE, 13 (4), PLOS, ISSN 1932-6203,

Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.

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Item Type: Article
Origin: Secondary publication via sponsored Golden Open Access
Title: Analysis of stochastic bifurcations with phase portraits
Language: English

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 of the journal: 13
Issue Number: 4
Place of Publication: Darmstadt
Publisher: PLOS
Classification DDC: 500 Naturwissenschaften und Mathematik > 530 Physik
Divisions: 05 Department of Physics > Institute for condensed matter physics (2021 merged in Institute for Condensed Matter Physics)
Date Deposited: 17 Apr 2019 14:26
Last Modified: 13 Dec 2022 11:03
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-86429
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/8642
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