Theoretical Analysis of Discreteness-Induced Transition in Autocatalytic Reaction Dynamics
Abstract
Transitions in the qualitative behavior of chemical reaction dynamics with a decrease in molecule number have attracted much attention. Here, a method based on a Markov process with a tridiagonal transition matrix is applied to the analysis of this transition in reaction dynamics. The transition to bistability due to the small-number effect and the mean switching time between the bistable states are analytically calculated in agreement with numerical simulations. In addition, a novel transition involving the reversal of the chemical reaction flow is found in the model under an external flow, and also in a three-component model. The generality of this transition and its correspondence to biological phenomena are also discussed.
Keywords
Cite
@article{arxiv.1403.6222,
title = {Theoretical Analysis of Discreteness-Induced Transition in Autocatalytic Reaction Dynamics},
author = {Nen Saito and Kunihiko Kaneko},
journal= {arXiv preprint arXiv:1403.6222},
year = {2015}
}
Comments
7 pages, 4 figures