TY  - GEN
A1  - Totz, Sonja Juliana
A1  - Löber, Jakob
A1  - Totz, Jan Frederik
A1  - Engel, Harald
T1  - Control of transversal instabilities in reaction-diffusion systems
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 962 
KW  - traveling waves
KW  - control
KW  - transversal instabilities
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-469762
SN  - 1866-8372
IS  - 962
ER  - 
TY  - JOUR
A1  - Totz, Sonja Juliana
A1  - Löber, Jakob
A1  - Totz, Jan Frederik
A1  - Engel, Harald
T1  - Control of transversal instabilities in reaction-diffusion systems
JF  - New journal of physics : the open-access journal for physics
N2  - 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.
KW  - traveling waves
KW  - control
KW  - transversal instabilities
Y1  - 2018
U6  - https://doi.org/10.1088/1367-2630/aabce5
SN  - 1367-2630
VL  - 20
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -