Control of transversal instabilities in reaction-diffusion systems

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Date
2018
Volume
20
Issue
5
Journal Title
Title
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Publisher
Bristol : Institute of Physics Publishing
Abstract

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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Keywords
control, transversal instabilities, traveling waves, Control engineering, Dynamic models, Photosensitivity, Piecewise linear techniques, Turbulence, Wave propagation, Belousov-Zhabotinsky reactions, FitzHugh-Nagumo model, Piecewise linear, Plane wave propagation, Reaction diffusion systems, Spiral turbulence, Traveling wave, Uncontrolled systems, Diffusion in liquids
Citation
Totz, S., Löber, J., Totz, J. F., & Engel, H. (2018). Control of transversal instabilities in reaction-diffusion systems. 20(5). https://doi.org//10.1088/1367-2630/aabce5
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License
CC BY 3.0 Unported