Instability of boundary equilibrium for Reaction-Diffusion system of a complex-balanced reaction network

TL;DR

This paper investigates the stability properties of boundary and positive equilibria in reaction-diffusion systems modeling complex-balanced chemical networks, providing conditions for convergence to stable states.

Contribution

It offers new analysis of boundary equilibrium instability and proves convergence to positive equilibria in general reversible reaction-diffusion networks.

Findings

Boundary equilibria are locally unstable in certain stoichiometric classes.

Solutions starting near positive equilibria tend to converge to them.

The results apply to a broad class of reversible reaction-diffusion systems.

Abstract

In this paper we study the local instability to the boundary equilibria and the local stability to the positive equilibria for some chemical reaction-diffusion systems. We first analyze a three-species system with boundary equilibria in some stoichiometric classes. Then We prove the convergence to the positive equilibria for a general reversible reaction-diffusion network as long as the initial data is closed enough to the the positive equilibria.