Relation between the convective field and the stationary probability distribution of chemical reaction networks

We investigate the relation between the stationary probability distribution of chemical reaction systems and the convective field derived from the chemical Fokker-Planck equation (CFPE) by comparing predictions of the convective field to the results of stochastic simulations based on Gillespie'...

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Bibliographic Details
Published inNew journal of physics Vol. 22; no. 3; pp. 33012 - 33025
Main Authors Becker, Lara, Mendler, Marc, Drossel, Barbara
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.03.2020
Subjects
Algorithms
bifurcation theory
Chemical reactions
Computer simulation
dynamical systems
Fokker-Planck equation
Hopf bifurcation
intrinsic stochasticity
Physics
Probability distribution
Probability theory
reaction networks
Two dimensional models
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Summary:We investigate the relation between the stationary probability distribution of chemical reaction systems and the convective field derived from the chemical Fokker-Planck equation (CFPE) by comparing predictions of the convective field to the results of stochastic simulations based on Gillespie's algorithm. The convective field takes into account the drift term of the CFPE and the reaction bias introduced by the diffusion term. For one-dimensional systems, fixed points and bifurcations of the convective field correspond to extrema and phenomenological bifurcations of the stationary probability distribution whenever the CFPE is a good approximation to the stochastic dynamics. This provides an efficient way to calculate the effect of system size on the number and location of probability maxima and their phenomenological bifurcations in parameter space. For two-dimensional systems, we study models that have saddle-node and Hopf bifurcations in the macroscopic limit. Here, the existence of two stable fixed points of the convective field correlates either with two peaks of the stationary probability distribution, or with a peak and a shoulder. In contrast, a Hopf bifurcation that occurs in the convective field for decreasing system size is not accompanied by the onset of a crater-shaped probability distribution; decreasing system size rather destroys craters and replaces them by local maxima.
Bibliography:NJP-111197.R2
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ab73c6