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dc.contributor.authorMincheva, Maya
dc.contributor.authorRoussel, Marc R.
dc.date.accessioned2013-02-04T22:43:28Z
dc.date.available2013-02-04T22:43:28Z
dc.date.issued2006-11-22
dc.identifier.citationMincheva, Maya "A graph‑theoretic method for detecting potential Turing bifurcations," with Marc Roussel, J. Chem. Phys. 125 (20): Art. No. 204102, 2006.en_US
dc.identifier.issn0021-9606
dc.identifier.urihttp://commons.lib.niu.edu/handle/10843/13403
dc.identifier.urihttp://hdl.handle.net/10843/13403
dc.description.abstractThe 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.en_US
dc.language.isoen_USen_US
dc.publisherAmerican Institute of Physicsen_US
dc.subjectTuring bifurcationsen_US
dc.titleA graph-theoretic method for detecting potential Turing bifurcationsen_US
dc.typeArticleen_US
dc.altlocation.urihttp://dx.doi.org/10.1063/1.2397073en_US
dc.contributor.departmentDepartment of Mathematical Sciences


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