Differential and graphical approaches to multistability theory for chemical reaction networks

TL;DR

This paper synthesizes and expands mathematical results on multistability in chemical reaction networks, emphasizing a cycle-based theorem that offers insights into multiple equilibria with minimal computation.

Contribution

It consolidates and extends the theory of multistability in CRNs, highlighting a key cycle-based theorem and its connections to related results.

Findings

Cycle-based theorem provides conditions for multiple equilibria.

Mathematical synthesis simplifies analysis of complex CRNs.

Connections among various multistability results are clarified.

Abstract

The use of mathematical models has helped to shed light on countless phenomena in chemistry and biology. Often, though, one finds that systems of interest in these fields are dauntingly complex. In this paper, we attempt to synthesize and expand upon the body of mathematical results pertaining to the theory of multiple equilibria in chemical reaction networks (CRNs), which has yielded surprising insights with minimal computational effort. Our central focus is a recent, cycle-based theorem by Gheorghe Craciun and Martin Feinberg, which is of significant interest in its own right and also serves, in a somewhat restated form, as the basis for a number of fruitful connections among related results.