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December 2009 Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements
Murad Banaji, Gheorghe Craciun
Commun. Math. Sci. 7(4): 867-900 (December 2009).


We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrix- and graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite multigraph, termed the “DSR graph”, is shown to be a useful representation of an interaction network when discussing questions of injectivity. A graph-theoretic condition, developed previously in the context of chemical reaction networks, is shown to be sufficient to guarantee injectivity for a large class of systems. The graph-theoretic condition is simple to state and often easy to check. Examples are presented to illustrate the wide applicability of the theory developed.


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Murad Banaji. Gheorghe Craciun. "Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements." Commun. Math. Sci. 7 (4) 867 - 900, December 2009.


Published: December 2009
First available in Project Euclid: 25 January 2010

zbMATH: 1195.05038
MathSciNet: MR2604624

Primary: 05C38 , 05C50 , 15A15 , 34C99

Keywords: chemical reactions , Injectivity , Interaction networks , multiple equilibria , network structure , SR graph

Rights: Copyright © 2009 International Press of Boston


Vol.7 • No. 4 • December 2009
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