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. © 1996 The American Physical Society.

• Received 4 March 1996

DOI:https://doi.org/10.1103/PhysRevE.54.5522