Recurrent events of synchrony in complex networks of pulse-coupled oscillators

We present and analyze deterministic complex networks of pulse-coupled oscillators that exhibits recurrent events comprised of an increase and a decline in synchrony. Events emerging from the networks may form an oscillatory behavior or may be separated by periods of asynchrony with varying duration. The phenomenon is specific to spatial networks with both short- and long-ranged connections and requires delayed interactions and refractoriness of oscillators.