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.
Author details: | Sonja Juliana TotzORCiDGND, Jakob Löber, Jan Frederik TotzORCiD, Harald Engel |
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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): | CC-BY - Namensnennung 4.0 International |
External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |