Interplay between Contractivity and Monotonicity for Reaction Networks

TL;DR

This paper uncovers a new link between monotonicity and contractivity in reaction networks, introducing a broad class of weakly contractive networks with guaranteed global convergence, supported by computationally verifiable conditions and applications in biology.

Contribution

It introduces a novel relationship between monotonicity and contractivity, defining a new class of weakly contractive reaction networks with verifiable matrix conditions.

Findings

New class of weakly contractive reaction networks identified.

Unified proof of global convergence for multiple network classes.

Applications demonstrated in biological systems and signaling pathways.

Abstract

We establish a new relationship between monotonicity and contractivity and use this connection to describe a new general class of weakly contractive reaction networks. The new class is characterized by the stoichiometry matrix of the reaction network admitting a precise matrix factorization that can be verified computationally. Reaction networks in this class are weakly contractive, implying global convergence to equilibria under appropriate technical conditions. Furthermore, we describe the novel subclass of cross-polytope networks. We also show that our results provide a unified proof of global convergence for several classes of networks previously studied in the literature. The practical relevance of the results is demonstrated by examples from systems biology and signaling pathways.