Partial synchronization in populations of pulse-coupled oscillators

TLDR

The study investigates the long‑term dynamics of all‑to‑all, noninstantaneous pulse‑coupled nonlinear oscillator populations. Fast excitatory coupling destabilizes both fully synchronized and asynchronous states, causing individual units to fire quasiperiodically while the network shows periodic firing, whereas inhibitory coupling fragments the network into variable numbers of fully synchronized clusters, with fast inhibition yielding many clusters and slow inhibition fewer, and networks of three or more units differ from two‑unit networks. © 1996 The American Physical Society.

Abstract

I study the long-term behavior of populations of nonlinear oscillators with all-to-all, noninstantaneous, pulse coupling. With fast enough excitatory coupling both the fully synchronized and the asynchronous state are unstable. In this case individual units fire quasiperiodically even though the network as a whole shows a periodic firing pattern. The behavior of networks with three or more units is different in this regard from that of two-unit networks. With inhibitory coupling the network can break up into a variable number of fully synchronized clusters. For fast inhibition the number of clusters tends to be large, while the number of clusters is smaller for slow inhibition. \textcopyright{} 1996 The American Physical Society.