Why Turing mechanism is an obstacle to stationary periodic patterns in bounded reaction-diffusion media with advection

Literature Information

Publication Date 2010-03-17
DOI 10.1039/B921918H
Impact Factor 3.676
Authors

Arik Yochelis, Moshe Sheintuch


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Abstract

Formation of stationary periodic patterns is paramount to many chemical, biological, physical, and ecological media. One of the most subtle mechanisms was suggested by Turing, who highlighted the applicability of isotropic reaction-diffusion dynamics with at least two diffusing fields. However, on finite domains with the presence of a symmetry breaking differential advection, two diffusing fields are rather disadvantageous to formation of stationary periodic patterns. We show that the criterion to stationary periodic patterns in Turing type models requires non-periodic boundary conditions and tuning of two parameters (a co-dimension-2 bifurcation in space) whereas in systems with one diffusing field (non-Turing) the bifurcation is of co-dimension 1 and thus easier to satisfy. We demonstrate this general result using spatial dynamics methods and direct numerical simulations of the canonical FitzHugh-Nagumo model.

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Physical Chemistry Chemical Physics

Physical Chemistry Chemical Physics
CiteScore: 5.5
Self-citation Rate: 10.3%
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Physical Chemistry Chemical Physics (PCCP) is an international journal co-owned by 19 physical chemistry and physics societies from around the world. This journal publishes original, cutting-edge research in physical chemistry, chemical physics and biophysical chemistry. To be suitable for publication in PCCP, articles must include significant innovation and/or insight into physical chemistry; this is the most important criterion that reviewers and Editors will judge against when evaluating submissions. The journal has a broad scope and welcomes contributions spanning experiment, theory, computation and data science. Topical coverage includes spectroscopy, dynamics, kinetics, statistical mechanics, thermodynamics, electrochemistry, catalysis, surface science, quantum mechanics, quantum computing and machine learning. Interdisciplinary research areas such as polymers and soft matter, materials, nanoscience, energy, surfaces/interfaces, and biophysical chemistry are welcomed if they demonstrate significant innovation and/or insight into physical chemistry. Joined experimental/theoretical studies are particularly appreciated when complementary and based on up-to-date approaches.

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