DOI: 10.5061/dryad.kh18932g1
title: Data from: Asymmetric autocatalytic reactions and their stationary distribution

description: 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 Bibbona, Kim, Wiuf (J.Roy.Soc.Interface, 2020) with 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 Induces Transitions regime, the formula provides the fraction
 of time spent at each of the stable points.
description: The data consists of simulations based on the Gillespie
 stochastic algorithm for Markov chain models of chemical reactions, the
 description of which is available on Wikipedia: https://en.wikipedia.org/wiki/Gillespie_algorithm The deposited file "GillespieSSa.nb" is a structured document of basic code for such an algorithm created by Wolfram Research Mathematica, an application used for mathematical and scientific computation. Instructions for opening such files are available in the documentation of the Mathematica application: https://reference.wolfram.com/workbench/index.jsp?topic=/com.wolfram.eclipse.help/html/tasks/notebook/edit.html "To open a notebook file in the Mathematica source editor one should <strong>select the notebook and right-click, choosing Open With &gt; Mathematica Source Editor</strong>. When the notebook has opened it should appear in the editor pane. At this stage one can work with the textual form of the notebook.  
description: # Asymmetric autocatalytic reactions and their stationary distribution
 [https://doi.org/10.5061/dryad.kh18932g1](https://doi.org/10.5061/dryad.kh18932g1) # Description of the data and file structure The paper uses simulated data generated by a stochastic simulation algorithm. We used Mathematica code to implement a standard Gillespie algorithm for the chemical reaction network modeled by a continuous Markov chain. ## Code/Software The file includes the complete Mathematica code for the simulation algorithm we used to generate data in our paper. The deposited file GillespieSSa.nb is a structured document created by Wolfram Research Mathematica, an application used for mathematical and scientific computation. Instructions for opening such files are available in the documentation of the Mathematica application: https://reference.wolfram.com/workbench/index.jsp?topic=/com.wolfram.eclipse.help/html/tasks/notebook/edit.html "To open a notebook file in the Mathematica source editor one should **select the notebook and right-click, choosing Open With &gt; Mathematica Source Editor**. When the notebook has opened it should appear in the editor pane. At this stage one can work with the textual form of the notebook.”