  We show that long chaotic transients dominate the dynamics of randomly
diluted networks of pulse-coupled oscillators. This contrasts with the rapid
convergence towards limit cycle attractors found in networks of globally
coupled units. The lengths of the transients strongly depend on the network
connectivity and varies by several orders of magnitude, with maximum transient
lengths at intermediate connectivities. The dynamics of the transient exhibits
a novel form of robust synchronization. An approximation to the largest
Lyapunov exponent characterizing the chaotic nature of the transient dynamics
is calculated analytically.

Disordered Systems and Neural Networks;Neurons and Cognition