Isochronous Dynamics in Pulse Coupled Oscillator Networks with Delay

P. Li, W. Lin, and K. Efstathiou
Chaos, 27(5), 053103, 2017
DOI: 10.1063/1.4982794
Arxiv preprint

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Abstract

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 fixed values of the network parameters each such isochronous region corresponds to a subset of initial states on an appropriate surface of section with non-zero dimension 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 a proof of its existence, and describe its properties. We further describe other isochronous regions that appear in the system.