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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.
13, In: PLOS ONE, (4), PLOS, ISSN 1932-6203,
DOI: 10.1371/journal.pone.0196126,
Secondary publishing via sponsored Golden Open Access, [Article]

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Item Type: Article
Origin: Secondary publishing via sponsored Golden Open Access
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
Classification DDC: 500 Naturwissenschaften und Mathematik > 530 Physik
Divisions: 05 Department of Physics > Institute for condensed matter physics
Date Deposited: 17 Apr 2019 14:26
Last Modified: 21 Jan 2020 15:30
DOI: 10.1371/journal.pone.0196126
URN: urn:nbn:de:tuda-tuprints-86429
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/8642
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