Prevalence of unstable attractors in networks of pulse-coupled oscillators

Preprint

25 February 2002

preprint
Published by arXiv in arXiv

Abstract

We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for large networks and a wide range of parameters. They are enclosed by basins of attraction of other attractors but are remote from their own basin volume such that arbitrarily small noise leads to a switching among attractors.

Keywords

PULSE COUPLED OSCILLATORS
UNSTABLE ATTRACTORS
NETWORKS OF PULSE
DYNAMICAL SYSTEM
PREVALENCE

All Related Versions

Version 1, 2002-02-25, ArXiv
Version 2, 2002-10-01, ArXiv
Published version: Physical Review Letters, 89 (15), 154105.

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