Synchronization in complex networks

Pikovsky, 2001

Osipov, 2007

Hall, 1983

S.H. Strogatz, Obituaries. Arthur T. Winfree, 2003

Wiener, 1948

Winfree, 1967, Biological rhythms and the behavior of populations of coupled oscillators, J. Theoret. Biol., 16, 15, 10.1016/0022-5193(67)90051-3

Winfree, 1980

Ariaratnam, 2001, Phase diagram for the winfree model of coupled nonlinear oscillators, Phys. Rev. Lett., 86, 4278, 10.1103/PhysRevLett.86.4278

Watts, 1998, Collective dynamics of ‘small-world’ networks, Nature (London), 393, 440, 10.1038/30918

Travers, 1969, An experimental study of the small world problem, Sociometry, 32, 425, 10.2307/2786545

Strogatz, 2001, Exploring complex networks, Nature (London), 410, 268, 10.1038/35065725

Albert, 2002, Statistical mechanics of complex networks, Rev. Mod. Phys., 74, 47, 10.1103/RevModPhys.74.47

Dorogovtsev, 2002, Evolution of networks, Adv. Phys., 51, 1079, 10.1080/00018730110112519

Newman, 2003, The structure and function of complex networks, SIAM Rev., 45, 167, 10.1137/S003614450342480

Boccaletti, 2006, Complex networks: Structure and dynamics, Phys. Rep., 424, 175, 10.1016/j.physrep.2005.10.009

Costa, 2007, Characterization of complex networks: A survey of measurements, Adv. Phys., 56, 167, 10.1080/00018730601170527

Erdös, 1959, On random graphs, Publ. Math. Debrecen, 6, 290, 10.5486/PMD.1959.6.3-4.12

Barabási, 1999, Emergence of scaling in random networks, Science, 286, 509, 10.1126/science.286.5439.509

Danon, 2005, Comparing community structure identification, J. Stat. Mech., 9, 8

Newman, 2004, Finding and evaluating community structure in networks, Phys. Rev. E, 69, 026113, 10.1103/PhysRevE.69.026113

Girvan, 2002, Community structure in social and biological networks, Proc. Natl. Acad. Sci. USA, 99, 7821, 10.1073/pnas.122653799

Guimerà, 2003, Self-similar community structure in organisations, Phys. Rev. E, 68, 065103, 10.1103/PhysRevE.68.065103

Guimerà, 2005, The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles, Proc. Natl. Acad. Sci. USA, 102, 7794, 10.1073/pnas.0407994102

Newman, 2006, Modularity and community structure in networks, Proc. Natl. Acad. Sci. USA, 103, 8577, 10.1073/pnas.0601602103

Strogatz, 1988, Collective synchronisation in lattices of nonlinear oscillators with randomness, J. Phys. A: Math. Gen., 21, L699, 10.1088/0305-4470/21/13/005

Niebur, 1991, Oscillator-phase coupling for different two-dimensional network connectivities, Phys. Rev. A, 44, 6895, 10.1103/PhysRevA.44.6895

Strogatz, 2000, From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D, 143, 1, 10.1016/S0167-2789(00)00094-4

Acebrón, 2005, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys., 77, 137, 10.1103/RevModPhys.77.137

Kuramoto, 1975, Self-entrainment of a population of coupled nonlinear oscillators, vol. 39, 420

Kuramoto, 1984

Restrepo, 2005, Onset of synchronization in large networks of coupled oscillators, Phys. Rev. E, 71, 036151, 10.1103/PhysRevE.71.036151

Motter, 2005, Network synchronization, diffusion, and the paradox of heterogeneity, Phys. Rev. E, 71, 016116, 10.1103/PhysRevE.71.016116

Watts, 1999

Hong, 2002, Synchronization on small-world networks, Phys. Rev. E, 65, 026139, 10.1103/PhysRevE.65.026139

Moreno, 2004, Synchronization of Kuramoto oscillators in scale-free networks, Europhys. Lett., 68, 603, 10.1209/epl/i2004-10238-x

Moreno, 2004, Fitness for synchronization of network motifs, Physica A, 343, 279, 10.1016/j.physa.2004.05.033

S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, Critical phenomena in complex networks, Rev. Mod. Phys

Marro, 1999

Gómez-Gardeñes, 2007, Paths to synchronization on complex networks, Phys. Rev. Lett., 98, 034101, 10.1103/PhysRevLett.98.034101

Gómez-Gardeñes, 2007, Synchronizability determined by coupling strengths and topology on Complex Networks, Phys. Rev. E, 75, 066106, 10.1103/PhysRevE.75.066106

McGraw, 2005, Clustering and the synchronization of oscillator networks, Phys. Rev. E, 72, 015101, 10.1103/PhysRevE.72.015101

McGraw, 2007, Analysis of nonlinear synchronization dynamics of oscillator networks by laplacian spectral methods, Phys. Rev. E, 75, 027104, 10.1103/PhysRevE.75.027104

Gómez-Gardeñes, 2007, Synchronization in networks with variable local properties, Internat. J. Bifurc. Chaos, 17, 2501, 10.1142/S0218127407018579

Restrepo, 2005, Synchronization in large directed networks of coupled phase oscillators, Chaos, 16, 015107, 10.1063/1.2148388

Restrepo, 2006, Emergence of synchronization in large complex networks of interacting dynamical systems, Physica D, 224, 114, 10.1016/j.physd.2006.08.026

Ichinomiya, 2004, Frequency synchronization in a random oscillator network, Phys. Rev. E, 70, 026116, 10.1103/PhysRevE.70.026116

Ichinomiya, 2005, Path-integral approach to dynamics in a sparse random network, Phys. Rev. E, 72, 016109, 10.1103/PhysRevE.72.016109

Lee, 2005, Synchronization transition in scale-free networks: Clusters of synchrony, Phys. Rev. E, 72, 026208, 10.1103/PhysRevE.72.026208

Moreno, 2002, Epidemic outbreaks in complex heterogeneous networks, Eur. Phys. J. B, 26, 521, 10.1140/epjb/e20020122

Oh, 2007, Synchronization transition of heterogeneously coupled oscillators on scale-free networks, Phys. Rev. E, 75, 011104, 10.1103/PhysRevE.75.011104

Gómez-Gardeñes, 2006, From scale-free to Erdös–Rényi networks, Phys. Rev. E, 73, 056124, 10.1103/PhysRevE.73.056124

Almendral, 2007, Dynamical and spectral properties of complex networks, New J. Phys., 9, 187, 10.1088/1367-2630/9/6/187

Donetti, 2006, Optimal network topologies: Expanders, cages, Ramanujan graphs, entangled networks and all that, J. Stat. Mech., 8, 7

Oh, 2005, Modular synchronization in complex networks, Phys. Rev. E, 72, 047101, 10.1103/PhysRevE.72.047101

Arenas, 2006, Synchronization reveals topological scales in complex networks, Phys. Rev. Lett., 96, 114102, 10.1103/PhysRevLett.96.114102

Arenas, 2006, Synchronization processes in complex networks, Physica D, 224, 27, 10.1016/j.physd.2006.09.029

Lodato, 2007, Synchronization properties of network motifs, Europhys. Lett., 78, 28001, 10.1209/0295-5075/78/28001

Gfeller, 2008, Spectral coarse graining and synchronization in oscillator networks, Phys. Rev. Lett., 100, 174104, 10.1103/PhysRevLett.100.174104

Arenas, 2007, Synchronization and modularity in complex networks, Eur. Phys. J. ST, 143, 19, 10.1140/epjst/e2007-00066-2

Gleiser, 2006, Synchronization and structure in an adaptive oscillator network, Eur. Phys. J. B, 53, 233, 10.1140/epjb/e2006-00362-y

Boccaletti, 2007, Detecting complex network modularity by dynamical clustering, Phys. Rev. E, 75, 045102, 10.1103/PhysRevE.75.045102

Radicchi, 2006, Entrainment of coupled oscillators on regular networks by pacemakers, Phys. Rev. E, 73, 036218, 10.1103/PhysRevE.73.036218

Kori, 2004, Entrainment of randomly coupled oscillator networks by a pacemaker, Phys. Rev. Lett., 93, 254101, 10.1103/PhysRevLett.93.254101

Guardiola, 2000, Synchronization, diversity, and topology of networks of integrate and fire oscillators, Phys. Rev. E, 62, 5565, 10.1103/PhysRevE.62.5565

Roxin, 2004, Self-sustained activity in a small-world network of excitable neurons, Phys. Rev. Lett., 92, 198101, 10.1103/PhysRevLett.92.198101

Lago-Fernández, 2000, Fast response and temporal coherent oscillations in small-world networks, Phys. Rev. Lett., 84, 2758, 10.1103/PhysRevLett.84.2758

Hodgkin, 1952, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117, 500, 10.1113/jphysiol.1952.sp004764

Golomb, 2000, The number of synaptic inputs and the synchrony of large sparse neuronal networks, Neural Comput., 12, 1095, 10.1162/089976600300015529

Leyva, 2006, Sparse repulsive coupling enhances synchronization in complex networks, Phys. Rev. E, 74, 056112, 10.1103/PhysRevE.74.056112

Vragovic, 2006, Performance of excitable small-world networks of Bonhoeffer–van der Pol–FitzHugh–Nagumo oscillators, Europhys. Lett., 76, 780, 10.1209/epl/i2006-10351-x

Cartwright, 2000, Phys. Rev. E, 62, 1149, 10.1103/PhysRevE.62.1149

Denker, 2004, Breaking synchrony by heterogeneity in complex networks, Phys. Rev. Lett., 92, 074103, 10.1103/PhysRevLett.92.074103

Gade, 1996, Synchronization of oscillators with random nonlocal connectivity, Phys. Rev. E, 54, 64, 10.1103/PhysRevE.54.64

Gade, 2000, Synchronous chaos in coupled map lattices with small-world interactions, Phys. Rev. E, 62, 6409, 10.1103/PhysRevE.62.6409

Batista, 2003, Mode locking in small-world networks of coupled circle maps, Physica A, 322, 118, 10.1016/S0378-4371(02)01917-9

Ott, 1993

Jost, 2002, Spectral properties and synchronization in coupled map lattices, Phys. Rev. E, 65, 016201, 10.1103/PhysRevE.65.016201

Lind, 2004, Coherence in scale-free networks of chaotic maps, Phys. Rev. E, 70, 056207, 10.1103/PhysRevE.70.056207

Dorogovtsev, 2002, Pseudofractal scale-free web, Phys. Rev. E, 65, 066122, 10.1103/PhysRevE.65.066122

Andrade, 2005, Apollonian networks: Simultaneously scale-free, small world, Euclidean, space filling, and with matching graphs, Phys. Rev. Lett., 94, 018702, 10.1103/PhysRevLett.94.018702

Atay, 2004, Delays, connection topology, and synchronization of coupled chaotic maps, Phys. Rev. Lett., 92, 144101, 10.1103/PhysRevLett.92.144101

Masoller, 2005, Random delays and the synchronization of chaotic maps, Phys. Rev. Lett., 94, 134102, 10.1103/PhysRevLett.94.134102

Martí, 2006, Chaotic maps coupled with random delays: Connectivity, topology, and network propensity for synchronization, Physica A, 371, 104, 10.1016/j.physa.2006.04.093

Jalan, 2003, Self-organized and driven phase synchronization in coupled maps, Phys. Rev. Lett., 90, 014101, 10.1103/PhysRevLett.90.014101

Amritkar, 2003, Self-organized and driven phase synchronization in coupled map networks, Physica A, 321, 220, 10.1016/S0378-4371(02)01750-8

Jalan, 2005, Synchronized clusters in coupled map networks. I. Numerical studies, Phys. Rev. E, 72, 016211, 10.1103/PhysRevE.72.016211

Levnajic, 2007, 633

Li, 2004, Phase synchronization in small-world networks of chaotic oscillators, Physica A, 341, 73, 10.1016/j.physa.2004.04.112

Yook, 2006, Synchronization of rössler oscillators on scale-free topolgies, Physica A, 371, 781, 10.1016/j.physa.2006.04.116

Belykh, 2004, Blinking model and synchronization in small-world networks with a time-varying coupling, Physica D, 195, 188, 10.1016/j.physd.2004.03.013

Barahona, 2002, Synchronization in small-world systems, Phys. Rev. Lett., 89, 054101, 10.1103/PhysRevLett.89.054101

Pecora, 1998, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80, 2109, 10.1103/PhysRevLett.80.2109

Fink, 2000, Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays, Phys. Rev. E, 61, 5080, 10.1103/PhysRevE.61.5080

Parker, 1989

Motter, 2005, Enhancing complex-network synchronization, Europhys. Lett., 69, 334, 10.1209/epl/i2004-10365-4

Nishikawa, 2006, Maximum performance at minimum cost in network synchronization, Physica D, 224, 77, 10.1016/j.physd.2006.09.007

Hwang, 2005, Synchronization in complex networks with age ordering, Phys. Rev. Lett., 94, 138701, 10.1103/PhysRevLett.94.138701

Monasson, 1999, Diffusion, localization and dispersion relations on small-world lattices, Eur. Phys. J. B, 12, 555, 10.1007/s100510051038

Matías, 1998, Transient periodic rotating waves and fast propagation of synchronization in linear arrays of chaotic systems, Phys. Rev. Lett., 81, 4124, 10.1103/PhysRevLett.81.4124

Hong, 2004, Factors that predict better synchronizability on complex networks, Phys. Rev. E, 69, 067105, 10.1103/PhysRevE.69.067105

Bollobás, 2001

Newman, 2001, Random graphs with arbitrary degree distributions and their applications, Phys. Rev. E, 64, 026118, 10.1103/PhysRevE.64.026118

Nishikawa, 2003, Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?, Phys. Rev. Lett., 91, 014101, 10.1103/PhysRevLett.91.014101

Pecora, 2005, Synchronization of oscillators in complex networks, Chaos Complexity Lett., 1, 61

Wang, 2002, IEEE Trans. Circuits Syst. I, 49, 44

Wu, 2003, IEEE Trans. Circuits Syst. I, 50, 294, 10.1109/TCSI.2002.808215

Stephan, 2000, Computational analysis of functional connectivity between areas of primate cerebral cortex, Philos. Trans. R. Soc. London, Ser. B, 355, 111, 10.1098/rstb.2000.0552

Kaiser, 2006, Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems, PloS Comput. Biol., 2, 95, 10.1371/journal.pcbi.0020095

Cohen, 2003, Scale-free networks are ultrasmall, Phys. Rev. Lett., 90, 058701, 10.1103/PhysRevLett.90.058701

Newman, 2000, Mean-field solution of the small-world network model, Phys. Rev. Lett., 84, 3201, 10.1103/PhysRevLett.84.3201

Zhou, 2006, Universality in the synchronization of weighted random networks, Phys. Rev. Lett., 96, 034101, 10.1103/PhysRevLett.96.034101

Kim, 2007, Ensemble averageability in network spectra, Phys. Rev. Lett., 98, 248701, 10.1103/PhysRevLett.98.248701

Goh, 2001, Universal behavior of load distribution in scale-free networks, Phys. Rev. Lett., 87, 278701, 10.1103/PhysRevLett.87.278701

Barthélemy, 2004, Betweenness centrality in large complex networks, Eur. Phys. J. B, 38, 163, 10.1140/epjb/e2004-00111-4

Zhao, 2006, Relations between average distance, heterogeneity and network synchronizability, Physica A, 371, 773, 10.1016/j.physa.2006.03.041

Zhou, 2006, Hierarchical synchronization in complex networks with heterogeneous degrees, Chaos, 16, 015104, 10.1063/1.2150381

Zhou, 2006, Dynamical weights and enhanced synchronization in adaptive complex networks, Phys. Rev. Lett., 96, 164102, 10.1103/PhysRevLett.96.164102

Steyvers, 2005, The large-scale structure of semantic networks: Statistical analyses and a model for semantic growth, Cognitive Sci., 29, 41, 10.1207/s15516709cog2901_3

Kim, 2004, Performance of networks of artificial neurons: The role of clustering, Phys. Rev. E, 69, 045101, 10.1103/PhysRevE.69.045101

Newman, 2002, Assortative mixing in networks, Phys. Rev. Lett., 89, 208701, 10.1103/PhysRevLett.89.208701

Newman, 2003, Mixing patterns in networks, Phys. Rev. E, 67, 026126, 10.1103/PhysRevE.67.026126

di Bernardo, 2007, Effects of degree correlation on the synchronization of networks of oscillators, Internat. J. Bifurc. Chaos, 17, 3499, 10.1142/S0218127407019263

Chung, 2003, Spectra of random graphs with given expected degrees, Proc. Natl. Acad. Sci. USA, 100, 6313, 10.1073/pnas.0937490100

Wu, 2005, Synchronizability of networks of chaotic systems coupled via a graph with a prescribed degree sequence [rapid communication], Phys. Lett. A, 346, 281, 10.1016/j.physleta.2005.07.089

Atay, 2006, Synchronization of networks with prescribed degree distributions, IEEE Trans. Circuits Syst. I, 53, 92, 10.1109/TCSI.2005.854604

Atay, 2006, Network synchronization: Spectral versus statistical properties, Physica D, 224, 35, 10.1016/j.physd.2006.09.018

L. Donetti, P.I. Hurtado, M.A. Muñoz, Networks synchronization: Optimal and pessimal scale-free topologies, Arxiv eprint 0710.4886

Fiedler, 1973, Algebraic connectivity of graphs, Czech. Math. J., 23, 298, 10.21136/CMJ.1973.101168

Anderson, 1985, Eigenvalues of the Laplacian of a graph, Linear Multilinear Algebra, 18, 141, 10.1080/03081088508817681

Mohar, 1991, The laplacian spectrum of graphs, 871

Chung, 1997, vol. 92

Mohar, 1991, Eigenvalues, diameter, and mean distance in graphs, Graph Combinator., 7, 53, 10.1007/BF01789463

Mohar, 1989, Isoperimetric numbers of graphs, J. Combin. Theory Ser. B, 47, 274, 10.1016/0095-8956(89)90029-4

Cheeger, 1970, A lower bound for the smallest eigenvalue of the laplacian, Probl. Anal., 195

Huang, 2006, Abnormal synchronization in complex clustered networks, Phys. Rev. Lett., 97, 164101, 10.1103/PhysRevLett.97.164101

Zhou, 2006, Phase synchronization on scale-free networks with community structure, Phys. Lett. A, 368, 431, 10.1016/j.physleta.2007.04.083

Barrat, 2004, The architecture of complex weighted networks, Proc. Natl. Acad. Sci. USA, 101, 3747, 10.1073/pnas.0400087101

Yook, 2001, Weighted evolving networks, Phys. Rev. Lett., 86, 5835, 10.1103/PhysRevLett.86.5835

Newman, 2001, Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality, Phys. Rev. E, 64, 016132, 10.1103/PhysRevE.64.016132

Braunstein, 2003, Optimal paths in disordered complex networks, Phys. Rev. Lett., 91, 168701, 10.1103/PhysRevLett.91.168701

Felleman, 1991, Distributed hierarchical processing in the primate cerebral cortex, Cereb. Cortex, 1, 1, 10.1093/cercor/1.1.1-a

Scannell, 1999, The connectional organization of the cortico-thalamic system of the cat, Cereb. Cortex, 9, 277, 10.1093/cercor/9.3.277

Grenfell, 2001, Travelling waves and spatial hierarchies in measles epidemics, Nature (London), 414, 716, 10.1038/414716a

Grassly, 2005, Host immunity and synchronized epidemics of syphilis across the United States, Nature (London), 433, 417, 10.1038/nature03072

Kim, 2007, Spectral densities of scale-free networks, Chaos, 17, 6115, 10.1063/1.2735019

Macdonald, 2005, Minimum spanning trees of weighted scale-free networks, Europhys. Lett., 72, 308, 10.1209/epl/i2005-10232-x

Chavez, 2005, Synchronization is enhanced in weighted complex networks, Phys. Rev. Lett., 94, 218701, 10.1103/PhysRevLett.94.218701

Dorogovtsev, 2000, Structure of growing networks with preferential linking, Phys. Rev. Lett., 85, 4633, 10.1103/PhysRevLett.85.4633

Motter, 2005, Weighted networks are more synchronizable: How and why, Vol. 776, 201

Wang, 2007, Enhancing synchronization based on complex gradient networks, Phys. Rev. E, 75, 056205, 10.1103/PhysRevE.75.056205

Zhao, 2006, Better synchronizability predicted by a new coupling method, Eur. Phys. J. B, 53, 375, 10.1140/epjb/e2006-00383-6

Zou, 2006, Synchronizability of weighted aging scale-free networks, Phys. Rev. E, 74, 046107, 10.1103/PhysRevE.74.046107

Li, 2007, Enhancing synchronizability by weight randomization on regular networks, Eur. Phys. J. B, 57, 423, 10.1140/epjb/e2007-00189-0

Zhao, 2005, Enhanced synchronizability by structural perturbations, Phys. Rev. E, 72, 057102, 10.1103/PhysRevE.72.057102

Yin, 2006, Decoupling process for better synchronizability on scale-free networks, Phys. Rev. E, 74, 047102, 10.1103/PhysRevE.74.047102

Donetti, 2005, Entangled networks, synchronization, and optimal network topology, Phys. Rev. Lett., 95, 188701, 10.1103/PhysRevLett.95.188701

Guo, 2007, Chin. Phys. Lett., 24, 2437, 10.1088/0256-307X/24/8/077

Nishikawa, 2006, Synchronization is optimal in nondiagonalizable networks, Phys. Rev. E, 73, 065106, 10.1103/PhysRevE.73.065106

Lu, 2007, Enhanced synchronizability via age-based coupling, Phys. Rev. E, 76, 057103, 10.1103/PhysRevE.76.057103

Garlaschelli, 2004, Patterns of link reciprocity in directed networks, Phys. Rev. Lett., 93, 268701, 10.1103/PhysRevLett.93.268701

Zamora-Lopez, 2008, Reciprocity of networks with degree correlations and arbitrary degree sequences, Phys. Rev. E, 77, 016106, 10.1103/PhysRevE.77.016106

Bianconi, 2008, Local structure of directed networks, Phys. Rev. Lett., 100, 118701, 10.1103/PhysRevLett.100.118701

Brede, 2008, Locals vs. global synchronization in networks of non-identical kuramoto oscillators, Eur. Phys. J. B, 62, 87, 10.1140/epjb/e2008-00126-9

Motter, 2007, Introduction: Optimization in networks, Chaos, 17, 26101, 10.1063/1.2751266

Li, 2003, Synchronization and desynchronization of complex dynamical networks: An engineering viewpoint, IEEE Trans. Circuits Syst. I, 50, 1381, 10.1109/TCSI.2003.818611

Chen, 2006, Some simple synchronization criteria for complex dynamical networks, IEEE Trans. Circuits Syst. II, 53, 1185, 10.1109/TCSII.2006.882363

Wu, 1995, Application of kronecker products to the analysis of systems with uniform linear coupling, IEEE Trans. Circuits Syst. I, 42, 430

Belykh, 2004, Connection graph stability method for synchronized coupled chaotic systems, Physica D, 195, 159, 10.1016/j.physd.2004.03.012

Belykh, 2006, Synchronization in asymmetrically coupled networks with node balance, Chaos, 16, 5102, 10.1063/1.2146180

Li, 2006, Global synchronization and asymptotic stability of complex dynamical networks, IEEE Trans. Circuits Syst. II, 53, 28, 10.1109/TCSII.2005.854315

Chen, 2008, Chaos synchronization in complex networks, IEEE Trans. Circuits Syst. I, 55, 1335, 10.1109/TCSI.2008.916436

Elowitz, 2000, A synthetic oscillatory network of transcriptional regulators, Nature (London), 403, 335, 10.1038/35002125

García-Ojalvo, 2004, Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, Proc. Natl. Acad. Sci. USA, 101, 10955, 10.1073/pnas.0307095101

Wagemakers, 2006, Synchronization of electronic genetic networks, Chaos, 16, 3127, 10.1063/1.2173048

Koseska, 2007, Inherent multistability in arrays of autoinducer coupled genetic oscillators, Phys. Rev. E, 75, 031916, 10.1103/PhysRevE.75.031916

Strogatz, 2003

Chialvo, 1987, Non-linear dynamics of cardiac excitation and impulse propagation, Nature (London), 330, 749, 10.1038/330749a0

Fukuda, 2007, Synchronization of plant circadian oscillators with a phase delay effect of the vein network, Phys. Rev. Lett., 99, 098102, 10.1103/PhysRevLett.99.098102

Keith, 1963

Stenseth, 1999, Common dynamic structure of canada lynx populations within three climatic regions, Science, 285, 1071, 10.1126/science.285.5430.1071

Blasius, 1999, Complex dynamics and phase synchronization in spatially extended ecological systems, Nature (London), 399, 354, 10.1038/20676

Ranta, 1999, Ecology: A tale of big game and small bugs, Science, 285, 1022, 10.1126/science.285.5430.1022

Earn, 2000, Coherence and conservation, Science, 290, 1360, 10.1126/science.290.5495.1360

Moran, 1953, The statistical analysis of the canadian lynx cycle. ii. synchronization and meteorology, Aust. J. Zool. 1, 291, 10.1071/ZO9530291

Ripa, 2007, Biological filtering of correlated environments: Towards a generalised moran theorem, Oikos, 116, 783, 10.1111/j.0030-1299.2007.15497.x

Leibold, 2004, The metacommunity concept: A framework for multi-scale community ecology, Ecol. Lett., 7, 601, 10.1111/j.1461-0248.2004.00608.x

Maser, 2007, Weak trophic interactions and the balance of enriched metacommunities, J. Theor. Biol., 247, 337, 10.1016/j.jtbi.2007.03.003

Vandermeer, 2004, Coupled oscillations in food-webs: Balancing competition and mutualism in simple ecological models, Am. Nat., 163, 857, 10.1086/420776

Dunne, 2006, The network structure of food webs, 27

Binzegger, 2004, A quantitative map of the circuit of cat primary visual cortex, J. Neurosci., 24, 8441, 10.1523/JNEUROSCI.1400-04.2004

Silberberg, 2005, Synaptic pathways in neural microcircuits, Trends Neurosci., 28, 541, 10.1016/j.tins.2005.08.004

Markram, 2004, Interneurons of the neocortical inhibitory system, Nature Rev. Neurosci., 5, 793, 10.1038/nrn1519

Buzsáki, 2004, Interneuron diversity series: Circuit complexity and axon wiring economy of cortical interneurons, Trends Neurosci., 27, 186, 10.1016/j.tins.2004.02.007

Chklovskii, 2002, Wiring optimization in cortical circuits, Neuron, 34, 341, 10.1016/S0896-6273(02)00679-7

Karbowski, 2001, Optimal wiring principle and plateaus in the degree of separation for cortical neurons, Phys. Rev. Lett., 86, 3674, 10.1103/PhysRevLett.86.3674

Sik, 1995, Hippocampal CA1 interneurons: An in vivo intracellular labeling study, J. Neurosci., 15, 6651, 10.1523/JNEUROSCI.15-10-06651.1995

Braitenberg, 1998

Sik, 1994, Inhibitory ca1-ca3-hilar region feedback in the hippocampus, Science, 265, 1722, 10.1126/science.8085161

Fries, 2005, A mechanism for cognitive dynamics: Neuronal communication through neuronal coherence, Trends Cogn. Sci., 9, 474, 10.1016/j.tics.2005.08.011

Konig, 1996, Integrator or coincidence detector? The role of the cortical neuron revisited, Trends Neurosci., 19, 130, 10.1016/S0166-2236(96)80019-1

Buzsáki, 1995, Temporal structure in spatially organized neuronal ensembles: A role for interneuronal networks, Curr. Opin. Neurobiol., 5, 504, 10.1016/0959-4388(95)80012-3

Bassett, 2006, Small-world brain networks, The Neuroscientist, 12, 512, 10.1177/1073858406293182

Reijneveld, 2007, The application of graph theoretical analysis to complex networks in the brain, Clinical Neurophysiology, 118, 2317, 10.1016/j.clinph.2007.08.010

Sporns, 2004, Organization, development and function of complex brain networks, Trends Cogn. Sci., 8, 418, 10.1016/j.tics.2004.07.008

Sporns, 2004, The small world of the cerebral cortex, Neuroinformatics, 2, 145, 10.1385/NI:2:2:145

Hilgetag, 2000, Anatomicalconnectivity defines the organization of clusters of cortical areas in macaque monkey and cat, Philos. Trans. R. Soc. London, Ser. B., 355, 91, 10.1098/rstb.2000.0551

Hilgetag, 2004, Clustered organization of cortical connectivity, Neuroinformatics, 2, 353, 10.1385/NI:2:3:353

Stam, 2004, Functional connectivity patterns of human magnetoencephalographic recordings: A small-world network?, Neurosci. Lett., 355, 25, 10.1016/j.neulet.2003.10.063

Eguiluz, 2005, Scale-free brain functional networks, Phys. Rev. Lett., 94, 018102, 10.1103/PhysRevLett.94.018102

Salvador, 2005, Neurophysiological architecture of functional magnetic resonance images of human brain, Cereb. Cortex, 15, 1332, 10.1093/cercor/bhi016

Bassett, 2006, From the cover: Adaptive reconfiguration of fractal small-world human brain functional networks, Proc. Natl. Acad. Sci. USA, 103, 19518, 10.1073/pnas.0606005103

Zhou, 2006, Hierarchical organization unveiled by functional connectivity in complex brain networks, Phys. Rev. Lett., 97, 238103, 10.1103/PhysRevLett.97.238103

Zemanová, 2006, Structural and functional clusters of complex brain networks, Physica D, 224, 202, 10.1016/j.physd.2006.09.008

Zhou, 2007, Structure function relationship in complex brain networks expressed by hierarchical synchronization, New J. Phys., 9, 178, 10.1088/1367-2630/9/6/178

da Silva, 1974, Model of brain rhythmic activity, Kybernetik, 15, 27, 10.1007/BF00270757

Honey, 2007, Network structure of cerebral cortex shapes functional connectivity on multiple time scales, Proc. Natl. Acad. Sci. USA, 104, 10240, 10.1073/pnas.0701519104

Fox, 2005, The human brain is intrinsically organized into dynamic, anticorrelated functional networks, Proc. Natl. Acad. Sci. USA, 102, 9673, 10.1073/pnas.0504136102

Engel, 2001, Dynamic predictions: Oscillations and synchrony intop-down processing, Nature. Rev. Neurosci., 2, 705, 10.1038/35094565

Stam, 2005, Nonlinear dynamical analysis of eeg and meg: Review of an emerging field, Clin. Neurophysiol., 116, 2266, 10.1016/j.clinph.2005.06.011

Tass, 1998, Detection of n:m phase locking from noisy data: Application to magnetoencephalography, Phys. Rev. Lett., 81, 3291, 10.1103/PhysRevLett.81.3291

Lai, 2007, Characterization of synchrony with applications to epileptic brain signals, Phys. Rev. Lett., 98, 108102, 10.1103/PhysRevLett.98.108102

Popovych, 2006, Control of neuronal synchrony by nonlinear delayed feedback, Biol. Cybernetics., 95, 69, 10.1007/s00422-006-0066-8

Nicol, 1994, Parallel simulation today, Ann. Oper. Res., 53, 249, 10.1007/BF02136831

Guclu, 2006, Synchronization landscapes in small-world-connected computer networks, Phys. Rev. E, 73, 066115, 10.1103/PhysRevE.73.066115

Korniss, 2000, From massively parallel algorithms and fluctuating time horizons to nonequilibrium surface growth, Phys. Rev. Lett., 84, 1351, 10.1103/PhysRevLett.84.1351

Grinstein, 1993, Temporally periodic phases and kinetic roughening, Phys. Rev. Lett., 70, 3607, 10.1103/PhysRevLett.70.3607

Muñoz, 2003, Stochastic theory of synchronization transitions in extended systems, Phys. Rev. Lett., 90, 204101, 10.1103/PhysRevLett.90.204101

Edwards, 1982, The surface statistics of a granular aggregate, Proc. Roy. Soc. London, Ser. A, 381, 17, 10.1098/rspa.1982.0056

Barabási, 1995

Korniss, 2003, Suppressing roughness of virtual times in parallel discrete-event simulations, Science, 299, 677, 10.1126/science.1079382

Miyano, 2007, Data synchronization in a network of coupled phase oscillators, Phys. Rev. Lett., 98, 024102, 10.1103/PhysRevLett.98.024102

Olfati-Saber, 2004, Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49, 1520, 10.1109/TAC.2004.834113

Olfati-Saber, 2005, Ultrafast consensus in small-world networks, 2371

Wu, 2007, Consensus problem in multi-agent systems with physical position neighbourhood evolving network, Physica A, 379, 681, 10.1016/j.physa.2006.12.026

Hekmat, 2006

Sivrikaya, 2004, Time synchronization in sensor networks: A survey, Network, IEEE, 18, 45, 10.1109/MNET.2004.1316761

A. Díaz-Guilera, J. Gómez-Gardenes, Y. Moreno, M. Nekovee, Synchronization in random geometric graphs, Internat. J. Bifurc. Chaos (in press)

Simeone, 2007, Distributed time synchronization in wireless sensor networks with coupled discrete-time oscillators, EURASIP J. Wireless Commun. Network., 2007, 57054, 10.1155/2007/57054

Degesys, 2007, Desync: Self-organizing desynchronization and tdma on wireless sensor networks, 11

Díaz-Guilera, 2008, Phase patterns of coupled oscillators with application to wireless communication, vol. 5151, 172

Hong, 2004, Distributed change detection in large scale sensor networks through the synchronization of the pulse-coupled oscillators, 869

Nagatani, 2002, The physics of traffic jams, Rep. Prog. Phys., 65, 1331, 10.1088/0034-4885/65/9/203

Helbing, 2003, Modelling supply networks and business cycles as unstable transport phenomena, New J. Phys., 5, 90, 10.1088/1367-2630/5/1/390

Helbing, 2004, Physics, stability, and dynamics of supply networks, Phys. Rev. E, 70, 066116, 10.1103/PhysRevE.70.066116

Lämmer, 2006, Decentralised control of material or traffic flows in networks using phase-synchronisation, Physica A, 363, 39, 10.1016/j.physa.2006.01.047

Helbing, 2005, Self-organized control of irregular or perturbed network traffic, 239

Crucitti, 2004, A topological analysis of the Italian electric power grid, Physica A, 338, 92, 10.1016/j.physa.2004.02.029

Chassin, 2005, Evaluating North American electric grid reliability using the Barabási Albert network model, Physica A, 355, 667, 10.1016/j.physa.2005.02.051

Sachtjen, 2000, Disturbances in a power transmission system, Phys. Rev. E, 61, 4877, 10.1103/PhysRevE.61.4877

Crucitti, 2004, Model for cascading failures in complex networks, Phys. Rev. E, 69, 045104, 10.1103/PhysRevE.69.045104

Scirè, 2005, Dynamic modeling of the electric transportation network, Europhys. Lett., 71, 318, 10.1209/epl/i2004-10533-6

Symetricom, How time finally caught up with the power grid. White paper, 2003. http://www.symmttm.com/pdf/Gps/wp_PowerGrid.pdf

Filatrella, 2008, Analysis of a power grid using a Kuramoto-like model, Eur. Phys. J. B, 61, 485, 10.1140/epjb/e2008-00098-8

Buchanan, 2007

Pluchino, 2005, Changing opinions in a changing world: A new perspective in sociophysics, Internat. J. Modern Phys. C, 16, 515, 10.1142/S0129183105007261

Forbes, 2002, No contagion, only interdependence: Measuring stock market comovements, J. Fin., 57, 2223, 10.1111/0022-1082.00494

Mantegna, 1999, Hierarchical structure in financial markets, Eur. Phys. J. B, 11, 193, 10.1007/s100510050929

Onnela, 2003, Dynamics of market correlations: Taxonomy and portfolio analysis, Phys. Rev. E, 68, 056110, 10.1103/PhysRevE.68.056110

Basalto, 2005, Clustering stock market companies via chaotic map synchronization, Physica A, 345, 196, 10.1016/j.physa.2004.07.034

Serrano, 2003, Topology of the world trade web, Phys. Rev. E, 68, 015101, 10.1103/PhysRevE.68.015101

Garlaschelli, 2005, Structure and evolution of the world trade network, Physica A, 355, 138, 10.1016/j.physa.2005.02.075

Garlaschelli, 2007, Interplay between topology and dynamics in the World Trade Web, Eur. Phys. J. B, 57, 159, 10.1140/epjb/e2007-00131-6

Calderón, 2007, Trade intensity and business cycle synchronization: Are developing countries any different?, J. Int. Econ., 71, 2, 10.1016/j.jinteco.2006.06.001

Li, 2003, Complexity and synchronization of the world trade web, Physica A, 328, 287, 10.1016/S0378-4371(03)00567-3

Dorogovtsev, 2003, Spectra of complex networks, Phys. Rev. E, 68, 046109, 10.1103/PhysRevE.68.046109

Rodgers, 2005, Eigenvalue spectra of complex networks, J. Phys. A: Math. Gen., 38, 9431, 10.1088/0305-4470/38/43/003

Bandyopadhyay, 2007, Universality in complex networks: Random matrix analysis, Phys. Rev. E, 76, 026109, 10.1103/PhysRevE.76.026109

Restrepo, 2004, Spatial patterns of desynchronization bursts in networks, Phys. Rev. E., 69, 066215, 10.1103/PhysRevE.69.066215

Jeong, 2000, The large-scale organization of metabolic networks, Nature, 407, 651, 10.1038/35036627

Restrepo, 2008, Weighted percolation on directed networks, Phys. Rev. Lett., 100, 058701, 10.1103/PhysRevLett.100.058701

Restrepo, 2006, Characterizing the dynamical importance of network nodes and links, Phys. Rev. Lett., 97, 094102, 10.1103/PhysRevLett.97.094102

Rajan, 2006, Eigenvalue spectra of random matrices for neural networks, Phys. Rev. Lett., 97, 188104, 10.1103/PhysRevLett.97.188104

Bi, 2001, Synaptic modification by correlated activity: Hebb’s postulate revisited, Annu. Rev. Neurosci., 24, 139, 10.1146/annurev.neuro.24.1.139

Gross, 2008, Adaptive coevolutionary networks: A review, J. Royal Soc. Interface, 5, 259, 10.1098/rsif.2007.1229

Ito, 2001, Spontaneous structure formation in a network of chaotic units with variable connection strengths, Phys. Rev. Lett., 88, 028701, 10.1103/PhysRevLett.88.028701

Ito, 2003, Spontaneous structure formation in a network of dynamic elements, Phys. Rev. E, 67, 046226, 10.1103/PhysRevE.67.046226

Sorrentino, 2008, Adaptive synchronization of dynamics on evolving complex networks, Phys. Rev. Lett., 100, 114101, 10.1103/PhysRevLett.100.114101

Arenas, 2008, Motif-based communities in complex networks, J. Phys. A, 41, 224001, 10.1088/1751-8113/41/22/224001

Arenas, 2008, Multiple resolution of the modular structure of complex networks, New J. Phys., 10, 05039, 10.1088/1367-2630/10/5/053039