Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 7, Number 4 (2009), 867-900.
Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements
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.
Commun. Math. Sci. Volume 7, Number 4 (2009), 867-900.
First available in Project Euclid: 25 January 2010
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.) 05C38: Paths and cycles [See also 90B10] 34C99: None of the above, but in this section 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14]
Banaji, Murad; Craciun, Gheorghe. Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements. Commun. Math. Sci. 7 (2009), no. 4, 867--900. http://projecteuclid.org/euclid.cms/1264434136.