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Control of transversal instabilities in reaction-diffusion systems

  • In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh-Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov-Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.

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Metadaten
Author details:Sonja Juliana TotzORCiDGND, Jakob Löber, Jan Frederik TotzORCiD, Harald Engel
URN:urn:nbn:de:kobv:517-opus4-469762
DOI:https://doi.org/10.25932/publishup-46976
ISSN:1866-8372
Title of parent work (German):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
Publication series (Volume number):Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (962)
Publication type:Postprint
Language:English
Date of first publication:2020/07/01
Publication year:2018
Publishing institution:Universität Potsdam
Release date:2020/07/01
Tag:control; transversal instabilities; traveling waves
Issue:962
Number of pages:19
Source:New Journal of Physics 20 (2018) 053034 DOI: 10.1088/1367-2630/aabce5
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:Referiert
Publishing method:Open Access
License (German):License LogoCC-BY - Namensnennung 4.0 International
External remark:Bibliographieeintrag der Originalveröffentlichung/Quelle
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