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A graph-theoretic method for detecting potential Turing bifurcations
- Source :
- The Journal of chemical physics. 125(20)
- Publication Year :
- 2006
-
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.
- Subjects :
- Models, Molecular
Pure mathematics
Graph theoretic
General Physics and Astronomy
Graph
Enzymes
Substrate Specificity
Diffusion
Enzyme Activation
Models, Chemical
Nonlinear Dynamics
Enzyme Stability
Bipartite graph
Computer Simulation
Physical and Theoretical Chemistry
Turing
computer
Bifurcation
Algorithms
Mathematics
computer.programming_language
Subjects
Details
- ISSN :
- 00219606
- Volume :
- 125
- Issue :
- 20
- Database :
- OpenAIRE
- Journal :
- The Journal of chemical physics
- Accession number :
- edsair.doi.dedup.....af9cf5ffd76b7c343113cb443f53062a