# Seemingly stable chemical kinetics can be stable, marginally stable, or unstable

Source: [Seemingly stable chemical kinetics can be stable, marginally stable, or unstable](<https://www.sota2.com/research/paper/68fa55411e209131ce99243a>)

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

Data updated: 2025-10-25T13:27:41.818Z

Authors: Andrea Agazzi, Jonathan C. Mattingly

Published: 2018-10-15T17:55:20.000Z

## Abstract

We present three examples of chemical reaction networks whose ordinary differential equation scaling limit are almost identical and in all cases stable. Nevertheless, the Markov jump processes associated to these reaction networks display the full range of behaviors: one is stable (positive recurrent), one is unstable (transient) and one is marginally stable (null recurrent). We study these differences and characterize the invariant measures by Lyapunov function techniques. In particular, we design a natural set of such functions which scale homogeneously to infinity, taking advantage of the same scaling behavior of the reaction rates.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1810.06547>)

[PDF](<https://arxiv.org/pdf/1810.06547.pdf>)