Algebraic structures generating reaction-diffusion models: the activator-substrate system

TL;DR

This paper develops a class of nonlinear reaction-diffusion models based on algebraic structures, aiming to understand their integrability and stability properties related to pattern formation.

Contribution

It introduces an algebraic framework for constructing reaction-diffusion equations, linking algebraic structures to the models' integrability and stability features.

Findings

Algebraic skeletons can generate reaction-diffusion systems.

The approach provides insights into pattern formation stability.

Potential for algebraic classification of reaction-diffusion models.

Abstract

We shall construct a class of nonlinear reaction-diffusion equations starting from an infinitesimal algebraic skeleton. Our aim is to explore the possibility of an algebraic foundation of integrability properties and of stability of equilibrium states associated with nonlinear models describing patterns formation.