# Stochastic properties of systems controlled by autocatalytic reactions I

Source: [Stochastic properties of systems controlled by autocatalytic reactions I](<https://www.sota2.com/research/paper/68fa1e687a2b558e293223a6>)

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

Data updated: 2025-10-23T14:57:13.366Z

Authors: L. Pal

Published: 2004-04-16T17:10:10.000Z

## Abstract

We analyzed the stochastic behavior of systems controlled by autocatalytic reaction A+X -\> X+X. Assuming the distribution of reacting particles in the system volume to be uniform, we introduced the notion of the point model of reaction kinetics, and derived a system of differential equations for probabilities of finding n=0,1,... autocatalytic particles at a given time moment. It has been found that the kinetic law of the mass action cannot be supported by stochastic model.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0404402>)

[PDF](<https://arxiv.org/pdf/cond-mat/0404402.pdf>)