Some results on injectivity and multistationarity in chemical reaction networks

Abstract

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 results also mentioned. Several results appear in, or are close to, results in the literature. Here, we emphasise the connections between the results, and where possible, present elementary proofs which rely solely on basic linear algebra and calculus. 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.

final (uncorrected) accepted version

References in corpus (4)

• Injectivity, multiple zeros, and multistationarity in reaction networks
• Determinant Expansions of Signed Matrices and of Certain Jacobians
• Global convergence in systems of differential equations arising from chemical reaction networks
• Some results on the structure and spectra of matrix-products

Cited by in corpus (10)

• The smallest bimolecular mass action reaction networks admitting Andronov-Hopf bifurcation
• Unstable Cores are the source of instability in chemical reaction networks
• Oscillations in three-reaction quadratic mass-action systems
• Adding species to chemical reaction networks: preserving rank preserves nondegenerate behaviours
• Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity
• The disguised toric locus and affine equivalence of reaction networks
• Mixed volume of small reaction networks
• Building oscillatory chemical reaction networks by adding reversible reactions
• Structural conditions for saddle-node bifurcations in chemical reaction networks
• The inheritance of local bifurcations in mass action networks