  We investigate the stability of synchronization in networks of delay-coupled
excitable neural oscillators. On the basis of the master stability function
formalism, we demonstrate that synchronization is always stable for excitatory
coupling independently of the delay and coupling strength. Superimposing
inhibitory links randomly on top of a regular ring of excitatory coupling,
which yields a small-world-like network topology, we find a phase transition to
desynchronization as the probability of inhibitory links exceeds a critical
value. We explore the scaling of the critical value in dependence on network
properties. Compared to random networks, we find that small-world topologies
are more susceptible to desynchronization via inhibition.
