2015/01/15 by Sonja Molnos, Molnos, Sonja, Jakob Löber +5
Computer Science · Medicine · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Biological Physics (physics.bio-ph) #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.1501.03769
openalex publication_date 2015/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In two-dimensional reaction-diffusion systems, local curvature perturbations in the shape of traveling waves are typically damped out and disappear in the course of time. If, however, the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated wave shapes and to spreading spiral turbulence. For experimentally relevant parameter values, the photosensitive Belousov-Zhabotinsky reaction (PBZR) does not exhibit transversal wave instabilities. Here, we propose a mechanism to artificially induce these instabilities via a wave shape dependent spatio-temporal feedback loop, and study the emerging wave patterns. In numerical simulations with the modified Oregonator model for the PBZR using experimentally realistic parameter values we demonstrate the feasibility of this control scheme. Conversely, 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 stabilising flat wave propagation.