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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)
Article, Secondary publication

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

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Item Type: Article
Type of entry: Secondary publication
Title: Analysis of stochastic bifurcations with phase portraits
Language: English
Date: 17 April 2019
Place of Publication: Darmstadt
Year of primary publication: 2018
Publisher: PLOS
Journal or Publication Title: PLOS ONE
Volume of the journal: 13
Issue Number: 4
Corresponding Links:
Origin: Secondary publication via sponsored Golden Open Access

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
Classification DDC: 500 Science and mathematics > 530 Physics
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: 20 Oct 2023 09:04
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/8642
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