Optimization of synchronization in gradient clustered networks.

We consider complex clustered networks with a gradient structure, where the sizes of the clusters are distributed unevenly. Such networks describe actual networks in biophysical systems and in technological applications more closely than the previous models. Theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field, but only when the gradient field points from large to small clusters. A remarkable finding is that, if the gradient field is sufficiently strong, synchronizability of the network is mainly determined by the properties of the subnetworks in the two largest clusters. These results are verified by numerical eigenvalue analysis and by direct simulation of synchronization dynamics on coupled-oscillator networks.

[1]  G. Hu,et al.  Instability and controllability of linearly coupled oscillators: Eigenvalue analysis , 1998 .

[2]  M. A. O'Neil,et al.  The connectional organization of the cortico-thalamic system of the cat. , 1999, Cerebral cortex.

[3]  M P Young,et al.  Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[4]  Gary D Bader,et al.  Systematic identification of protein complexes in Saccharomyces cerevisiae by mass spectrometry , 2002, Nature.

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

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

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

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

[9]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[10]  Alessandro Vespignani,et al.  Large-scale topological and dynamical properties of the Internet. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  R. Karp,et al.  Conserved pathways within bacteria and yeast as revealed by global protein network alignment , 2003, Proceedings of the National Academy of Sciences of the United States of America.

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

[13]  L. Mirny,et al.  Protein complexes and functional modules in molecular networks , 2003, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[16]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[17]  T. Ideker.  A systems approach to discovering signaling and regulatory pathways--or, how to digest large interaction networks into relevant pieces. , 2004, Advances in experimental medicine and biology.

[18]  L. Holm,et al.  Unraveling protein interaction networks with near-optimal efficiency , 2004, Nature Biotechnology.

[19]  Mark Gerstein,et al.  Analyzing cellular biochemistry in terms of molecular networks. , 2003, Annual review of biochemistry.

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

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

[22]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

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

[24]  M Chavez,et al.  Synchronization in complex networks with age ordering. , 2005, Physical review letters.

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

[26]  Alex Arenas,et al.  Synchronization reveals topological scales in complex networks. , 2006, Physical review letters.

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

[28]  J. Kurths,et al.  Hierarchical synchronization in complex networks with heterogeneous degrees. , 2006, Chaos.

[29]  Changsong Zhou,et al.  Hierarchical organization unveiled by functional connectivity in complex brain networks. , 2006, Physical review letters.

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

[31]  Adilson E. Motter,et al.  Maximum performance at minimum cost in network synchronization , 2006, cond-mat/0609622.

[32]  Marcus Kaiser,et al.  Clustered organization of cortical connectivity , 2007, Neuroinformatics.

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

[34]  Olaf Sporns,et al.  The small world of the cerebral cortex , 2007, Neuroinformatics.

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

[36]  V. Latora,et al.  Detecting complex network modularity by dynamical clustering. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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