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Phys. Rev. E 74, 016102 (2006) [5 pages]

Synchronization in dynamical networks: Evolution along commutative graphs

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S. Boccaletti1, D.-U. Hwang1, M. Chavez2, A. Amann3, J. Kurths4, and L. M. Pecora5
1CNR- Istituto dei Sistemi Complessi, Largo E. Fermi, 6-50125 Florence, Italy
2Laboratoire de Neurosciences Cognitives et Imagerie Cérébrale (LENA) CNRS UPR-640, Hôpital de la Salpêtrière, 47 Boulevard de l'Hôpital, 75651 Paris CEDEX 13, France
3Tyndall National Institute, Lee Maltings, Cork, Ireland
4Institut für Physik, Universität Potsdam, Am Neuen Palais, PF 601553, D-14415 Potsdam, Germany
5Code 6362, Naval Research Laboratory, Washington, D.C. 20375, USA

Received 5 December 2006; revised 18 April 2006; published 5 July 2006

Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior.

© 2006 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.74.016102
DOI:
10.1103/PhysRevE.74.016102
PACS:
89.75.Hc, 05.45.Xt, 87.18.Sn
 
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