2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/83311Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global classification of two variable excitable reaction-diffusion systems. In particular, we claim that the topology of the underlying two-dimensional homogeneous dynamics can be used to organize the system's behavior.Revtex, 4 pages, 4 figuresPattern Formation and Solitonstext