Global Attractor of a coupled Two-Cell Brusselator Model

TL;DR

This paper proves the existence of a finite-dimensional global attractor for a coupled two-cell Brusselator reaction-diffusion system, using novel estimation and decomposition methods.

Contribution

It introduces new techniques to establish the absorbing property and asymptotic compactness for complex reaction-diffusion systems with cubic nonlinearities.

Findings

Existence of a global attractor for the coupled Brusselator model.

Finite Hausdorff and fractal dimensions of the attractor.

New estimation and decomposition methods for reaction-diffusion systems.

Abstract

In this work the existence of a global attractor for the solution semiflow of the coupled two-cell Brusselator model equations is proved. A grouping estimation method and a new decomposition approach are introduced to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of four-variable reaction-diffusion systems with cubic autocatalytic nonlinearity and with linear coupling. It is also proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite.