  Networks out of equilibrium display dynamics characterized by multiple
equilibria and sudden transitions. These transitions arise when each node
leaves its natural stable state and joins to an organized global activation
behavior. In this paper, we study local patterns near regime shifts in Network
Synchronization and Self-Organized Criticality (SOC) by a Koopman spectrum
data-driven approach. To illustrate these ideas, we use synchronized behavior
from an Integral-and-Fire oscillators (IFO) system and SOC in the Bak-Sneppen
model.
