Dynamics of two-compartment Gray–Scott equations Original Research Article

In this work the existence of a global attractor is proved for the solution semiflow of the coupled two-compartment Gray–Scott equations with the homogeneous Neumann boundary condition on a bounded domain of space dimension n≤3n≤3. The grouping estimation method combined with a new decomposition approach is introduced to overcome the difficulties in proving the absorbing property and the asymptotic compactness of this four-component reaction–diffusion systems with cubic autocatalytic nonlinearity and linear coupling. The finite dimensionality of the global attractor is also proved