Structural Stability and Stabilization of Solutions of the Reversible Three-Component Gray-Scott System

Abstract

This paper is concerned with the structural stability and stabilization of solutions to the three-component reversible Gray-Scott system under the Dirichlet or Neumann boundary conditions defined in a bounded domain of Rn for 1 <= n <= 3. We prove that each solution depends on changes in a coefficient of the ratio of the reverse and forward reaction rates for the autocatalytic reaction as well as proving the continuous dependence on the initial data. We also prove that under Dirichlet's boundary conditions, the system is stabilized to the stationary solution by finitely many Fourier modes.