The inheritance of nondegenerate multistationarity in chemical reaction networks

TL;DR

This paper investigates how the ability of chemical reaction networks to have multiple stable and unstable equilibria is inherited from subnetworks, providing new theoretical results mainly for mass action kinetics.

Contribution

It introduces a unified framework to determine inheritance of multistationarity in CRNs, including some novel modifications and generalizations beyond known results.

Findings

Inheritance of MPNE and MPSE in CRNs identified

New modifications for network construction shown to preserve multistationarity

Framework applicable mainly to mass action kinetics with potential for broader classes

Abstract

We study how the properties of allowing multiple positive nondegenerate equilibria (MPNE) and multiple positive linearly stable equilibria (MPSE) are inherited in chemical reaction networks (CRNs). Specifically, when is it that we can deduce that a CRN admits MPNE or MPSE based on analysis of its subnetworks? Using basic techniques from analysis we are able to identify a number of situations where MPNE and MPSE are inherited as we build up a network. Some of these modifications are known while others are new, but all results are proved using the same basic framework, which we believe will yield further results. The results are presented primarily for mass action kinetics, although with natural, and in some cases immediate, generalisation to other classes of kinetics.