Synchronization in small-world systems

We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and...

Full description

Saved in:
Bibliographic Details
Published in:Physical review letters 2002-07, Vol.89 (5), p.054101-054101, Article 054101
Main Authors: Barahona, Mauricio, Pecora, Louis M
Format: Article
Language:English
Subjects:
Models, Theoretical
Nerve Net
Neural Networks (Computer)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcuts translates into improved network synchronizability. Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes. However, the small-world property does not guarantee synchronizability: the synchronization threshold lies within the boundaries, but linked to the end of the small-world region.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.89.054101