  We investigate heterogeneous coupling delays in complex networks of excitable
elements described by the FitzHugh-Nagumo model. The effects of discrete as
well as of uni- and bimodal continuous distributions are studied with a focus
on different topologies, i.e., regular, small-world, and random networks. In
the case of two discrete delay times resonance effects play a major role:
Depending on the ratio of the delay times, various characteristic spiking
scenarios, such as coherent or asynchronous spiking, arise. For continuous
delay distributions different dynamical patterns emerge depending on the width
of the distribution. For small distribution widths, we find highly synchronized
spiking, while for intermediate widths only spiking with low degree of
synchrony persists, which is associated with traveling disruptions, partial
amplitude death, or subnetwork synchronization, depending sensitively on the
network topology. If the inhomogeneity of the coupling delays becomes too
large, global amplitude death is induced.
