Collective Dynamics for Network-Organized Identical Excitable Nodes

We investigate the collective dynamics of network-organized identical excitable nodes. We theoretically analyze the stability of the rest state and propose that there are two different transition paths: the stationary path and the oscillatory path. We find that, although the onset of collective dynamics strongly depend on the network topology, the local dynamics and how local nodes interact with each other decide the transition path and the involved bifurcation.