Classification of instabilities for the nonideal Brusselator model

TL;DR

This paper analyzes a thermodynamically consistent nonideal Brusselator reaction-diffusion system, revisiting classical instability classifications and revealing that only specific types occur, with pattern outcomes sensitive to instability interactions.

Contribution

It extends the Cross-Hohenberg classification to a nonideal, thermodynamically consistent Brusselator model, showing which instabilities can occur and how they influence pattern formation.

Findings

Only type I and III instabilities occur in the system.

Energetic contributions do not directly generate instabilities.

Pattern sensitivity depends on the relative strength of coexisting instabilities.

Abstract

We investigate a nonideal, thermodynamically consistent Brusselator reaction-diffusion (RD) system that explicitly incorporates molecular interactions among species in both the diffusion process and the underlying chemical reaction network. Within this framework, we systematically revisit the Cross-Hohenberg classification of instabilities to assess the feasibility and characteristics of the various types of instability arising from the interplay between entropic and energetic contributions. Our analysis demonstrates that only type I and type III instabilities (the Cross-Hohenberg classification) can occur in this system; Energetic contributions do not explicitly generate instabilities, but may implicitly control their occurrence through their influence on the fixed-point (steady-state) concentrations. In cases where instabilities of different types coexist, we show that the resulting patterns are highly sensitive to the relative strengths of the competing instabilities.