Effects of Weight Distribution on Synchronization in Small-world Network

Many social, biological and ecological systems are better described as weighted networks than binary networks. It was found recently that many real-world networks exhibited nonuniform weight distribution. In this paper, we propose a weighted small-world network model in which the weight distribution can be controlled, and we study the synchronization behavior in this network. We find that the synchronize ability is weaker in a small-world network with power-law weight distribution than that with random weight distribution.

[1]  J. Jost,et al.  Spectral properties and synchronization in coupled map lattices. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Petter Holme,et al.  Subnetwork hierarchies of biochemical pathways , 2002, Bioinform..

[3]  D. Cvetkovic,et al.  Spectra of Graphs: Theory and Applications , 1997 .

[4]  Martin H. Levinson.  Linked: The New Science of Networks , 2004 .

[5]  J. Kurths,et al.  Enhancing complex-network synchronization , 2004, cond-mat/0406207.

[6]  P. Hui,et al.  Weighted scale-free networks with stochastic weight assignments. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Chunguang Li,et al.  An evolving network model with community structure , 2005, physics/0510239.

[8]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[9]  Alessandro Vespignani,et al.  Weighted evolving networks: coupling topology and weight dynamics. , 2004, Physical review letters.

[10]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Gade,et al.  Synchronous chaos in coupled map lattices with small-world interactions , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  O. Sporns,et al.  Organization, development and function of complex brain networks , 2004, Trends in Cognitive Sciences.

[13]  C. Lee Giles,et al.  Self-Organization and Identification of Web Communities , 2002, Computer.

[14]  Duncan J. Watts,et al.  Six Degrees: The Science of a Connected Age , 2003 .

[15]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[16]  Marc Timme,et al.  Breaking synchrony by heterogeneity in complex networks. , 2003, Physical review letters.

[17]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[18]  Bo Hu,et al.  General dynamics of topology and traffic on weighted technological networks. , 2005, Physical review letters.

[19]  Juergen Kurths,et al.  Weighted networks are more synchronizable: how and why , 2005 .

[20]  L F Lago-Fernández,et al.  Fast response and temporal coherent oscillations in small-world networks. , 1999, Physical review letters.

[21]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[22]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[23]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[24]  Beom Jun Kim,et al.  Synchronization on small-world networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[26]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[27]  S. Boccaletti,et al.  Synchronization is enhanced in weighted complex networks. , 2005, Physical review letters.

[28]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[29]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.