On a Two Dimensional Reaction-Diffusion System with Hypercyclical Structure

Abstract

We study a hypercyclical reaction-diffusion system which arises in the modeling of catalytic networks and describes the emerging of cluster states. We construct single cluster solutions in full two-dimensional space and then establish their stability or instability in terms of the number N of components. We provide a rigorous analysis around the single cluster solutions, which is new for systems of this kind. Our results show that as N increases, the system becomes unstable.