Adapting synapses in pulse-coupled oscillators

The effects of synaptic depression and facilitation on synchronous states of coupled integrate-and-fire neurons are analysed. Through linear perturbation theory, a discrete Hopf bifurcation in the firing times is examined, and synchrony is seen to persist as the coupling is increased for large networks and/or fast synapses. Oscillator death, bursting, and pattern formation are known to arise through strong coupling instabilities and are shown to be affected by adapting synapses.