Towards a global classification of excitable reaction-diffusion systems
  Patterns 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. 
Silvina Ponce Dawson, Maria Veronica D'Angelo, and John E. Pearson