Some results on injectivity and multistationarity in chemical reaction networks

Murad Banaji, Casian Pantea

Published 2013-09-26, updated 2014-08-26Version 4

The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on the nature of the network and the reaction rates. The results are primarily linear algebraic or matrix-theoretic, with some graph-theoretic corollaries also mentioned. Where possible, elementary proofs are presented, and a number of examples are provided to illustrate the variety of subtly different conclusions which can be reached via different computations. In addition, many of the computations are implemented in a web-based open source platform, allowing the reader to test examples including and beyond those analysed in the paper.