Synchronization of Two Pulse-Coupled Oscillators

Abstract

There is a vast literature on the question when firing-triggered pulsatile signaling among neurons will lead to synchrony. In this chapter, we analyze the simplest formalization of this question. Perhaps the main worthwhile conclusion from the analysis presented here is that there is no general statement of the form “excitatory interactions synchronize” or “inhibitory interactions synchronize.” Whether or not pulse-coupling synchronizes depends on the detailed nature of the responses of the neurons to signals they receive; see Proposition 26.2. Approximately speaking, excitatory pulse-coupling synchronizes if the phase response is of type 2, or if there is strong refractoriness; this will be made precise in inequality (26.12).