Desynchronization, mode locking and bursting in strongly coupled integrate-and-fire oscillators

We show how a synchronized pair of integrate-and-fire neural oscillators with noninstantaneous synaptic interactions can destabilize in the strong coupling regime resulting in non-phase-locked behavior. In the case of symmetric inhibitory coupling, desynchronization produces an inhomogeneous state in which one of the oscillators becomes inactive (oscillator death). On the other hand, for asymmetric excitatory/inhibitory coupling, mode locking can occur leading to periodic bursting patterns. The consequences for large globally coupled networks is discussed.