# A graph-theoretic condition for delay stability of reaction systems

Source: [A graph-theoretic condition for delay stability of reaction systems](<https://www.sota2.com/research/paper/68fa581e1e209131ce9ab60c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T15:08:36.299Z

Authors: Gheorghe Craciun, Maya Mincheva, Casian Pantea, Polly Y. Yu

Published: 2021-05-16T00:50:55.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2105.07321>)

[PDF](<https://arxiv.org/pdf/2105.07321.pdf>)