Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses
Adaptation and Self-Organizing Systems
2009-03-12 v1
Abstract
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be predicted from the phase response of a single oscillator to a given impulsive perturbation. We present a theory based on phase reduction of a jump stochastic process describing a Poisson-driven limit-cycle oscillator, and verify the results through numerical simula- tions and electric circuit experiments. We also give a geometrical interpretation of the synchronizing mechanism, a perturbative expansion to the stationary phase distribution, and the diffusion limit of our jump stochastic model.
Keywords
Cite
@article{arxiv.0802.3758,
title = {Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses},
author = {Kensuke Arai and Hiroya Nakao},
journal= {arXiv preprint arXiv:0802.3758},
year = {2009}
}