Phase synchronization on scale-free networks with community structure

Abstract In this Letter, we propose a growing network model that can generate scale-free networks with a tunable community strength. The community strength, C, is directly measured by the ratio of the number of external edges to that of the internal ones; a smaller C corresponds to a stronger community structure. By using the Kuramoto model, we investigated the phase synchronization on this network and found an abnormal region ( C ⩽ 0.002 ), in which the network has even worse synchronizability than the unconnected case ( C = 0 ). On the other hand, the community effect will vanish when C exceeds 0.1. Between these two extreme regions, a stronger community structure will hinder global synchronization.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[2]  Beom Jun Kim,et al.  Factors that predict better synchronizability on complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Tao Zhou,et al.  Better synchronizability predicted by crossed double cycle. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Ying-Cheng Lai,et al.  Synchronization in complex networks with a modular structure. , 2006, Chaos.

[5]  S. Boccaletti,et al.  Synchronizing weighted complex networks. , 2006, Chaos.

[6]  Carroll,et al.  Synchronous chaos in coupled oscillator systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Hideo Hasegawa,et al.  Dynamical mean-field approximation to small-world networks of spiking neurons: from local to global and/or from regular to random couplings. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Changsong Zhou,et al.  Universality in the synchronization of weighted random networks. , 2006, Physical review letters.

[9]  Gade,et al.  Synchronization of oscillators with random nonlocal connectivity. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[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]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[13]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

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

[15]  Adilson E Motter,et al.  Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? , 2003, Physical review letters.

[16]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[17]  H. Jürgensen.  Synchronization , 2021, Inf. Comput..

[18]  Tao Zhou,et al.  Relations between average distance, heterogeneity and network synchronizability , 2006 .

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

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

[21]  Claudio Castellano,et al.  Defining and identifying communities in networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[22]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[23]  Michael Menzinger,et al.  Clustering and the synchronization of oscillator networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[25]  Monika Sharma,et al.  Chemical oscillations , 2006 .

[26]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[27]  Bambi Hu,et al.  Epidemic spreading in community networks , 2005 .

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

[29]  Wang Bing-Hong,et al.  Synchronizability of Highly Clustered Scale-Free Networks , 2006 .

[30]  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.

[31]  A. Mikhailov,et al.  Mutual synchronization and clustering in randomly coupled chaotic dynamical networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Wen-Xu Wang,et al.  Collective synchronization induced by epidemic dynamics on complex networks with communities. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[34]  S. Redner,et al.  Connectivity of growing random networks. , 2000, Physical review letters.

[35]  E Oh,et al.  Modular synchronization in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Tao Zhou,et al.  Better synchronizability predicted by a new coupling method , 2006 .

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

[38]  Wenxu Wang,et al.  Enhanced synchronizability by structural perturbations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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