Longtime Dynamics of The Oregonator System

TL;DR

This paper proves the existence of a finite-dimensional global attractor and an exponential attractor for the Oregonator reaction-diffusion system, a mathematical model of the Belousov-Zhabotinskii reaction, demonstrating long-term stability properties.

Contribution

It introduces a new rescaling and grouping estimation method to establish the absorbing property and asymptotic compactness of the system's solutions.

Findings

Existence of a finite-dimensional global attractor.

Existence of an exponential attractor.

Demonstration of long-term stability of the system.

Abstract

In this work the existence and properties of a global attractor for the solution semiflow of the Oregonator system are proved. The Oregonator system is the mathematical model of the famous Belousov-Zhabotinskii reaction. A rescaling and grouping estimation method is developed to show the absorbing property and the asymptotic compactness of the solution trajectories of this three-variable reaction-diffusion system with quadratic nonlinearity from the autocatalytic kinetics. It is proved that the fractal dimension of the global attractor is finite. The existence of an exponential attractor for this Oregonator semiflow is also shown.