A graph-theoretic condition for delay stability of reaction systems

TL;DR

This paper establishes a graph-theoretic criterion based on cycles in the species-reaction graph that guarantees delay stability in reaction systems, ensuring stability regardless of rate constants and delays.

Contribution

It introduces a novel graph-theoretic condition for delay stability in reaction systems, applicable even when delays are absent, advancing understanding of stability in chemical kinetics.

Findings

The condition guarantees delay stability independent of rate constants and delays.

It applies to systems with no delay, ensuring asymptotic stability.

Cycle analysis in the species-reaction graph determines stability criteria.

Abstract

Delay mass-action systems provide a model of chemical kinetics when past states influence the current dynamics. In this work, we provide a graph-theoretic condition for delay stability, i.e., linear stability independent of both rate constants and delay parameters. In particular, the result applies when the system has no delay, implying asymptotic stability for the ODE system. The graph-theoretic condition is about cycles in the directed species-reaction graph of the network, which encodes how different species in the system interact.