Nondegenerate multistationarity in small reaction networks

TL;DR

This paper investigates conditions under which small chemical reaction networks can have multiple stable positive steady states, focusing on nondegenerate solutions and providing results that guide analysis of larger networks.

Contribution

It provides the first characterization of nondegenerate multistationarity in small reaction networks, advancing understanding of steady states in chemical kinetics.

Findings

Characterized nondegenerate multistationarity in small networks

Established criteria for the existence of multiple positive steady states

Provided techniques applicable to larger networks

Abstract

Much attention has been focused in recent years on the following algebraic problem arising from applications: which chemical reaction networks, when taken with mass-action kinetics, admit multiple positive steady states? The interest behind this question is in steady states that are stable. As a step toward this difficult question, here we address the question of multiple nondegenerate positive steady states. Mathematically, this asks whether certain families of parametrized, real, sparse polynomial systems ever admit multiple positive real roots that are simple. Our main results settle this problem for certain types of small networks, and our techniques point the way forward for larger networks.