Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions

TL;DR

This paper investigates non-Gaussian fluctuations in autocatalytic reactions using an extended van Kampen expansion, successfully capturing third moments and validating the approach through numerical simulations.

Contribution

It extends the van Kampen perturbative scheme beyond second order to analyze non-Gaussian fluctuations in autocatalytic reaction systems.

Findings

Theoretical predictions match simulation results well.

Third moments effectively characterize non-Gaussianity.

Method captures fluctuations in a four-population autocatalytic system.

Abstract

A stochastic model of autocatalytic chemical reactions is studied both numerically and analytically. The van Kampen perturbative scheme is implemented, beyond the second order approximation, so to capture the non Gaussianity traits as displayed by the simulations. The method is targeted to the characterization of the third moments of the distribution of fluctuations, originating from a system of four populations in mutual interaction. The theory predictions agree well with the simulations, pointing to the validity of the van Kampen expansion beyond the conventional Gaussian solution.