Lower bounds for positive roots and regions of multistationarity in chemical reaction networks

TL;DR

This paper develops a framework to identify explicit conditions under which real sparse polynomial systems, modeling biochemical networks, exhibit multiple positive solutions, indicating multistationarity.

Contribution

It introduces a general method to find explicit coefficients leading to multistationarity in polynomial systems, applied specifically to biochemical reaction networks.

Findings

Explicit coefficients for multistationarity in biochemical networks

Conditions for multiple positive solutions in polynomial systems

Application to reaction rate constants and conservation laws

Abstract

Given a real sparse polynomial system, we present a general framework to find explicit coefficients for which the system has more than one positive solution, based on the recent article by Bihan, Santos and Spaenlehauer. We apply this approach to find explicit reaction rate constants and total conservation constants in biochemical reaction networks for which the associated dynamical system is multistationary.