On a two-dimensional reaction-diffusion system with hypercyclical structure

We study a hypercyclical reaction-diffusion system which arises in the modelling 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. AMS classification scheme numbers: 35B35, 92C40, 35B40.