Analysis of firing behaviors in networks of pulse-coupled oscillators with delayed excitatory coupling

Isochronous dynamics in pulse coupled oscillator networks with delay

We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions-subsets of the phase space filled with periodic orbits having the same period. For each fixed value of the network parameters, such an isochronous region corresponds to a subset of initial states on an appropriate surface of section with non-zero dimensions such that all periodic orbits in this set have qualitatively similar dynamical behaviour. We analytically and numerically study in detail such an isochronous region, give proof of its existence, and describe its properties. We further describe other isochronous regions that appear in the system.

Experimental verification of synchronization in pulse-coupled oscillators with a refractory period and frequency distribution

We propose herein globally pulse-coupled electronic-circuit oscillators with a refractory period and frequency distribution. The synchronization of such oscillators, which was analyzed by Konishi and Kokame [Chaos 18, 033132 (2008)], is verified by circuit experiments. Furthermore, we investigate a cluster state in the oscillators and analytically derive a simple condition to estimate the maximum possible number of clusters, which is confirmed by the circuit experiments.