# Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria

## TL;DR

This paper investigates the rate at which certain chemical reaction-diffusion systems with boundary equilibria converge to their complex balanced equilibrium, providing new insights into their stability and convergence behavior.

## Contribution

It introduces new convergence results for reaction-diffusion systems with boundary equilibria, including a three-species system and a general two-species network.

## Key findings

- Convergence to equilibrium is established for specific reaction-diffusion systems.
- The rate of convergence is characterized for systems with boundary equilibria.
- Results apply to systems with quadratic nonlinearities in the positive orthant.

## Abstract

In this paper we study the rate of convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. We first analyze a three-species system with boundary equilibria in some stoichiometric classes, and whose right hand side is bounded above by a quadratic nonlinearity in the positive orthant. We prove similar results on the convergence to the positive equilibrium for a fairly general two-species reversible reaction-diffusion network with boundary equilibria.