# Autocatalysis in Reaction Networks

Source: [Autocatalysis in Reaction Networks](<https://www.sota2.com/research/paper/68fa512a1e209131ce9718eb>)

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

Data updated: 2025-10-25T11:16:28.658Z

Authors: Abhishek Deshpande, Manoj Gopalkrishnan

Published: 2013-09-16T13:46:32.000Z

## Abstract

The persistence conjecture is a long-standing open problem in chemical reaction network theory. It concerns the behavior of solutions to coupled ODE systems that arise from applying mass-action kinetics to a network of chemical reactions. The idea is that if all reactions are reversible in a weak sense, then no species can go extinct. A notion that has been found useful in thinking about persistence is that of "critical siphon." We explore the combinatorics of critical siphons, with a view towards the persistence conjecture. We introduce the notions of "drainable" and "self-replicable" (or autocatalytic) siphons. We show that: every minimal critical siphon is either drainable or self-replicable; reaction networks without drainable siphons are persistent; and non-autocatalytic weakly-reversible networks are persistent. Our results clarify that the difficulties in proving the persistence conjecture are essentially due to competition between drainable and self-replicable siphons.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1309.3957>)

[PDF](<https://arxiv.org/pdf/1309.3957.pdf>)