Isochronous Dynamics in Pulse Coupled Oscillator Networks with Delay
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.
Keywords
Cite
@article{arxiv.1701.07626,
title = {Isochronous Dynamics in Pulse Coupled Oscillator Networks with Delay},
author = {Pan Li and Wei Lin and Konstantinos Efstathiou},
journal= {arXiv preprint arXiv:1701.07626},
year = {2017}
}