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arXiv · 2311.17979

Asymmetric autocatalytic reactions and their stationary distribution

Cameron Gallinger·Lea Popovic
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Abstract

We consider a general class of autocatalytic reactions, that has been shown to display stochastically switching behaviour (Discreteness Induced Transitions) in some parameter regimes. This behaviour was shown to occur when either the overall species count is low, or when the rate of inflow and outflow of species is relatively much smaller than the rate of autocatalytic reactions. The long-term behaviour of this class was analyzed in \cite{KBW20} with an analytic formula for the stationary distribution in the symmetric case. We focus on the case of asymmetric autocatalytic reactions and provide a formula for an approximate stationary distribution of the model. We show this distribution has different properties corresponding to the distinct behaviour of the process in the three parameter regimes. In the Discreteness Induced Transitions regime, the formula provides the fraction of time spent at each of the stable points.

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Cameron Gallinger, Lea Popovic. 2023-11-29. Asymmetric autocatalytic reactions and their stationary distribution. https://arxiv.org/abs/2311.17979

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