INFORMATION CHANGE THE WORLD

International Journal of Image, Graphics and Signal Processing(IJIGSP)

ISSN: 2074-9074 (Print), ISSN: 2074-9082 (Online)

Published By: MECS Press

IJIGSP Vol.2, No.1, Nov. 2010

Novel Approach to Cluster Synchronization in Kuramoto Oscillators

Full Text (PDF, 952KB), PP.30-38


Views:58   Downloads:0

Author(s)

Xin Biao Lu,Bu Zhi Qin

Index Terms

Cluster synchronization, global approach, local approach, Kuramoto model

Abstract

Cluster synchronization is investigated in different complex dynamical networks. Based on an extended Kuramoto model, a novel approach is proposed to make a complex dynamical network achieve cluster synchronization, where the critical coupling strength between connected may be obtained by global adaptive approach and local adaptive approach, respectively. The former approach only need know each node’s state and its destination state; while the latter approach need know the local information. Simulation results show the effectiveness of the distributed control strategy.

Cite This Paper

Xin Biao Lu,Bu Zhi Qin, "Novel Approach to Cluster Synchronization in Kuramoto Oscillators", IJIGSP, vol.2, no.1, pp.30-38, 2010.

Reference

[1]X B Lu, B Z Qin, Synchronization in complex networks, Nova Science Press, New York, 2011.

[2]S. H. Strogatz, “From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators”, Physica D, vol.143,pp. 1-20,2000.

[3]K. Kaneko, “Relevance of Clustering to Biological Networks”, Physica D vol. 75, pp.55-73,1994.

[4]N. F Rulkov., “Images of synchronized chaos: Experiments with circuits” Chaos, vol. 6, pp.262-279, 1996.

[5]M. I Rabinovich, et al., “Origin of coherent structures in a discrete chaotic medium” Phys.Rev. E, vol. 60, pp.1130-1133, 1999.

[6]D. H Zanette, A. S. Mikhailov, “Condensation in globally coupled populations of chaotic dynamical systems”, Phys.Rev. E, vol. 57, pp. 276-281, 1998.

[7]W. X Qin., G. Chen,“Coupling schemes for cluster synchronization in coupled Josephson equation”, Physica D, vol.197,pp.375-391,2004.

[8]V. N.Belykh, I.Belykh V., E. Mosekide, “Cluster synchronization modes in an ensemble of coupled chaotic oscillators”, Phys. Rev. E, vol. 63, 036216, 2001.

[9]S. Jalan, R. E Amrikar., C. K. Hu,“Synchronized clusters in coupled map networks. I. Numerical studies”, Phys. Rev. E, vol. 72, 016211, 2005.

[10]J Kurths., C Zhou., “Dynamical weights and enhanced synchronization in adaptive complex networks”, Physical Review Letters, vol.96, 164102, 2006.

[11]T Nishikawa, A E. Motter, “Synchronization is optimal in nondiagonalizable networks”, Physical Review E, vol. 73, 065106, 2006.

[12]J Zhou., J. A Lu., J. Lu, “Pinning adaptive synchronization of a general complex dynamical network”, IEEE Transactions on Automatic Control, vol. 51(4), pp. 652-656, 2006.

[13]P. D. Lellis, M. D. Bernardo, F. Garofalo, “Novel decentralized adaptive strategies for the synchronization of complex networks”, Automatica, vol.45, pp.1312-1318, 2009.

[14]W L Lu. Chaos, “Adaptive dynamical networks via neighborhood information: Synchronization and pinning control”, vol.17(2), 23122, 2007.

[15]Q. S. Ren, J. Y. Zhao “Adaptive coupling and enhanced synchronization in coupled phase oscillators”, Phys. Rev. E. vol.76 016207, 2007.

[16]A L Barabasi, R Albert. "Emergence of scaling in random networks," Science.vol. 286, pp.509-512, 1999.

[17]D J Watts, S H Strogatz. “Collective dynamics of "smallworld" networks”, Nature. Vol. 393, pp.440-442, 1998.

[18]W. W. Zachary, “An information flow model for conflict and fission in small groups”, Journal of anthropological research, vol.33, pp.452-473, 1977.