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.
Publié le : 2009-12-15
Classification:
Interaction networks,
chemical reactions,
injectivity,
SR graph,
network structure,
multiple equilibria,
05C50,
05C38,
34C99,
15A15
@article{1264434136,
author = {Banaji, Murad and Craciun, Gheorghe},
title = {Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements},
journal = {Commun. Math. Sci.},
volume = {7},
number = {1},
year = {2009},
pages = { 867-900},
language = {en},
url = {http://dml.mathdoc.fr/item/1264434136}
}
Banaji, Murad; Craciun, Gheorghe. Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements. Commun. Math. Sci., Tome 7 (2009) no. 1, pp. 867-900. http://gdmltest.u-ga.fr/item/1264434136/