Graph operations and synchronization of complex networks
- 25 July 2005
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 72 (1), 016217
- https://doi.org/10.1103/physreve.72.016217
Abstract
The effects of graph operations on the synchronization of coupled dynamical systems are studied. The operations range from addition or deletion of links to various ways of combining networks and generating larger networks from simpler ones. Methods from graph theory are used to calculate or estimate the eigenvalues of the Laplacian operator, which determine the synchronizability of continuous or discrete time dynamics evolving on the network. Results are applied to explain numerical observations on random, scale-free, and small-world networks. An interesting feature is that, when two networks are combined by adding links between them, the synchronizability of the resulting network may worsen as the synchronizability of the individual networks is improved. Similarly, adding links to a network may worsen its synchronizability, although it decreases the average distance in the graph.This publication has 18 references indexed in Scilit:
- Delays, Connection Topology, and Synchronization of Coupled Chaotic MapsPhysical Review Letters, 2004
- Synchronization and desynchronization of complex dynamical networks: an engineering viewpointIEEE Transactions on Circuits and Systems I: Regular Papers, 2003
- Spectral properties and synchronization in coupled map latticesPhysical Review E, 2001
- Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arraysPhysical Review E, 2000
- Renormalization group analysis of the small-world network modelPhysics Letters A, 1999
- Master Stability Functions for Synchronized Coupled SystemsPhysical Review Letters, 1998
- Synchronization of oscillators with random nonlocal connectivityPhysical Review E, 1996
- Coupled maps on treesPhysical Review E, 1995
- Coalescence, majorization, edge valuations and the laplacian spectra of graphsLinear and Multilinear Algebra, 1990
- Synchronization in chaotic systemsPhysical Review Letters, 1990