Onset of synchronization in complex gradient networks.

Recently, it has been found that the synchronizability of a scale-free network can be enhanced by introducing some proper gradient in the coupling. This result has been obtained by using eigenvalue-spectrum analysis under the assumption of identical node dynamics. Here we obtain an analytic formula for the onset of synchronization by incorporating the Kuramoto model on gradient scale-free networks. Our result provides quantitative support for the enhancement of synchronization in such networks, further justifying their ubiquity in natural and in technological systems.

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

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

[3]  P. Villon,et al.  Mechanical field interpolation , 2005 .

[4]  M E J Newman,et al.  Identity and Search in Social Networks , 2002, Science.

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

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

[7]  Ying-Cheng Lai,et al.  Enhancing synchronization based on complex gradient networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[9]  Edward Ott,et al.  Synchronization in large directed networks of coupled phase oscillators. , 2005, Chaos.

[10]  B. Kahng,et al.  Modular synchronization in complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  J. Kurths,et al.  Network synchronization, diffusion, and the paradox of heterogeneity. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[13]  Y. Lai,et al.  Jamming in complex gradient networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Sergei Maslov,et al.  Modularity and extreme edges of the internet. , 2003, Physical review letters.

[15]  E. Ott,et al.  Onset of synchronization in large networks of coupled oscillators. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Y. Lai,et al.  Abnormal synchronization in complex clustered networks. , 2006, Physical review letters.

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

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

[19]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

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

[21]  Y. Lai,et al.  Optimization of synchronization in gradient clustered networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Alex Arenas,et al.  Paths to synchronization on complex networks. , 2006, Physical review letters.

[23]  Kevin E. Bassler,et al.  Network dynamics: Jamming is limited in scale-free systems , 2004, Nature.

[24]  Changsong Zhou,et al.  Dynamical weights and enhanced synchronization in adaptive complex networks. , 2006, Physical review letters.

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

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

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

[28]  Y. Lai,et al.  Large-scale structural organization of social networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[30]  Steven H. Strogatz,et al.  Sync: The Emerging Science of Spontaneous Order , 2003 .

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

[32]  A. Motter,et al.  Synchronization is optimal in nondiagonalizable networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Chris Arney.  Sync: The Emerging Science of Spontaneous Order , 2007 .

[34]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[35]  Ying-Cheng Lai,et al.  Transition to global synchronization in clustered networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.