Loss of synchronization in complex neuronal networks with delay

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.