Document Type
Article
Abstract
The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical Modeling (Nauka, Moscow, 1987) (in Russian), p. 57] for Turing instabilities in a mass-action reaction-diffusion system involving n substances. The method is based on the representation of a reaction mechanism as a bipartite graph with two types of nodes representing chemical species and reactions, respectively. The condition for diffusion-driven instability is related to the existence of a structure in the graph known as a critical fragment. The technique is illustrated using a substrate-inhibited bifunctional enzyme mechanism which involves seven chemical species.
DOI
10.1063/1.2397073
Publication Date
11-22-2006
Recommended Citation
Mincheva, Maya "A graph‑theoretic method for detecting potential Turing bifurcations," with Marc Roussel, J. Chem. Phys. 125 (20): Art. No. 204102, 2006.
Original Citation
Mincheva, Maya "A graph‑theoretic method for detecting potential Turing bifurcations," with Marc Roussel, J. Chem. Phys. 125 (20): Art. No. 204102, 2006.
Legacy Department
Department of Mathematical Sciences
ISSN
0021-9606
Language
eng
Publisher
American Institute of Physics
