# Intrinsic fluctuations of chemical reactions with different approaches

## TL;DR

This paper compares different theoretical approaches to analyze intrinsic fluctuations in chemical reactions modeled by the Brusselator, highlighting discrepancies near bifurcation points and the limitations of linearized Langevin equations.

## Contribution

It systematically evaluates the accuracy of master, Langevin, and linearized Langevin methods for chemical reaction fluctuations, especially near bifurcation points.

## Key findings

- Discrepancies between methods are negligible far from bifurcation.
- Significant differences appear near the bifurcation line.
- Linearized Langevin equations exhibit singularities at bifurcation, not seen in simulations.

## Abstract

The Brusselator model are used for the study of the intrinsic fluctuations of chemical reactions with different approaches. The equilibrium states of systems are assumed to be spirally stable in mean-field description, and two statistical measures of intrinsic fluctuations are analyzed by different theoretical methods, namely, the master, the Langevin, and the linearized Langevin equation. For systems far away from the Hopf bifurcation line, the discrepancies between the results of different methods are insignificant even for small system size. However, the discrepancies become noticeable even for large system size when systems are closed to the bifurcation line. In particular, the statistical measures possess singular structures for linearized Langevin equation at the bifurcation line, and the singularities are absent from the simulation results of the master and the Langevin equation.