The Library

Do small worlds synchronize fastest?

Tools

Grabow, Carsten, Hill, Steven M., Grosskinsky, Stefan and Timme, Marc. (2010) Do small worlds synchronize fastest? Europhysics Letters, Vol.90 (No.4). Article no. 48002. ISSN 0295-5075

Preview

PDF
WRAP_Grossinsky_Do_small_worlds.pdf - Accepted Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (457Kb)

Official URL: http://dx.doi.org/10.1209/0295-5075/90/48002

Abstract

Small-world networks interpolate between fully regular and fully random topologies and simultaneously exhibit large local clustering as well as short average path length. Small-world topology has therefore been suggested to support network synchronization. Here we study the asymptotic speed of synchronization of coupled oscillators in dependence on the degree of randomness of their interaction topology in generalized Watts-Strogatz ensembles. We find that networks with fixed in-degree synchronize faster the more random they are, with small worlds just appearing as an intermediate case. For any generic network ensemble, if synchronization speed is at all extremal at intermediate randomness, it is slowest in the small-world regime. This phenomenon occurs for various types of oscillators, intrinsic dynamics and coupling schemes. Copyright (c) EPLA, 2010

Item Type:

Journal Article

Subjects:

Q Science > QC Physics

Divisions:

Faculty of Science > Centre for Complexity Science
Faculty of Science > Mathematics

Library of Congress Subject Headings (LCSH):

Graphic methods, System analysis, Synchronization

Journal or Publication Title:

Europhysics Letters

Publisher:

EPL Association, European Physical Society

ISSN:

0295-5075

Official Date:

May 2010

Dates:

Date	Event
May 2010	Published

Volume:

Vol.90

Number:

No.4

Number of Pages:

Page Range:

Article no. 48002

Identification Number:

10.1209/0295-5075/90/48002

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Open Access

Funder:

Germany. Bundesministerium für Bildung und Forschung (BMBF), Max-Planck-Gesellschaft zur Förderung der Wissenschaften [Max Planck Society for the Advancement of Science], Engineering and Physical Sciences Research Council (EPSRC)

Grant number:

01GQ0430 (BMBF), EP/E501311/1 (EPSRC)

References:

[1] Pikovsky A., Rosenblum M. and Kurths J., Synchronization,
A universal concept in nonlinear sciences (Cambridge
Univ. Press, Cambridge, UK) 2001.
[2] Arenas A. et al., Physics Reports, 469 (2008) 93.
[3] Kanter I., Kinzel W. and Kanter E., Europhys. Lett.,
57 (2002) 141.
[4] Maistrenko Yu. et al., Phys. Rev. Lett., 93 (2004)
084102.
[5] Netoff T. et al., J. Neurosci., 24 (2004) 8075.
[6] Strogatz S., Nature, 410 (2001) 268.
[7] Nishikawa T. et al., Phys. Rev. Lett., 91 (2003) 014101.
[8] Pecora L. and Carroll T., Phys. Rev. Lett., 80 (1998)
2109.
[9] Watts D. and Strogatz S., Nature, 393 (1998) 440.
[10] Barahona M. and Pecora L. M., Phys. Rev. Lett., 89
(2002) 054101.
[11] Roxin A., Riecke H. and Solla S., Phys. Rev. Lett.,
92 (2004) 198101.
[12] Zumdieck A. et al., Phys. Rev. Lett., 93 (2004) 244103.
[13] Zillmer R. et al., Phys. Rev. E, 76 (2007) 046102.
[14] Jahnke S., Memmesheimer R.-M. and Timme M.,
Phys. Rev. Lett., 100 (2008) 048102.
[15] Denker M., Timme M., Diesmann M., Wolf F. and
Geisel T., Phys. Rev. Lett., 92 (2004) 074103.
[16] Zillmer R., Brunel N. and Hansel D., Phys. Rev. E.,
79 (2009) 031909.
[17] Timme M., Wolf F. and Geisel T., Phys. Rev. Lett.,
92 (2004) 074101.
[18] Timme M., Geisel T. and Wolf F., Chaos, 16 (2006)
015108.
[19] Qi G. X. et al., Phys. Rev. E, 77 (2008) 056205.
[20] Qi G. X. et al., Europhys. Lett., 82 (2008) 38003.
[21] Timme M., Europhys. Lett., 76 (2006) 367.
[22] Acebron J. et al., Rev. Mod. Phys., 77 (2005) 137.
[23] Fagiolo G., Phys. Rev. E, 76 (2007) 026107.
[24] Almendral J. A. and Diaz-Guilera A., New J. Phys.,
9 (2007) 1211.
[25] Mirollo R. and Strogatz S., SIAM J. Appl. Math., 50
(1990) 366.
[26] Motter A., Zhou C. and Kurths J., Phys. Rev. E,
71 (2005) 016116; Goh K. et al., Phys. Rev. Lett., 96
(2006) 018701; Lee S., Kim P. and Jeong H., Phys. Rev.
E, 73 (2006) 016102; Arenas A., Diaz-Guilera A. and
Perez-Vicente C. J., Phys. Rev. Lett., 96 (2006) 114102.
[27] Zhou C and Kurths. J, Chaos, 16 (2006) 015104.