Structural conditions for saddle-node bifurcations in chemical reaction networks

Abstract

Motivated by investigating multistationarity in biochemical systems, we address saddle-node bifurcations for chemical reaction networks endowed with general kinetics. At positive equilibria, we identify structural network conditions that guarantee the bifurcation behavior, and we develop a method to identify the proper bifurcation parameters. As a relevant example, we explicitly provide such bifurcation parameters for Michaelis-Menten and Hill kinetics. Examples of applications include reversible feedback cycles, the central carbon metabolism of Escherichia coli, and autocatalytic networks.