# Asymptotic stability of delayed complex balanced reaction networks with non-mass action kinetics

Source: [Asymptotic stability of delayed complex balanced reaction networks with non-mass action kinetics](<https://www.sota2.com/research/paper/68fa5c041e209131ce9cd7d3>)

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

Data updated: 2025-10-25T17:24:25.895Z

Authors: Mih\\'aly Andr\\'as V\\'aghy, G\\'abor Szederk\\'enyi

Published: 2024-06-29T10:03:53.000Z

## Abstract

We consider delayed chemical reaction networks with generalized kinetics of product form and show that complex balancing implies that within each positive stoichiometric compatibility class there is a unique positive equilibrium that is locally asymptotically stable relative to its class. The main tools of the proofs are respectively a version of the well-known classical logarithmic Lyapunov function applied to kinetic systems and its generalization to the delayed case as a Lyapunov-Krasovskii functional. Finally, we demonstrate our results through illustrative examples.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2407.00387>)

[PDF](<https://arxiv.org/pdf/2407.00387.pdf>)