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Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization
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Abstract Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous and reversible. Recently, however, explosive phenomena have been reported in complex networks’ structure and dynamics, which rather remind first-order (discontinuous and irreversible) transitions. Explosive percolation, which was discovered in 2009, corresponds to an abrupt change in the network’s structure, and explosive synchronization (which is concerned, instead, with the abrupt emergence of a collective state in the networks’ dynamics) was studied as early as the first models of globally coupled phase oscillators were taken into consideration. The two phenomena have stimulated investigations and debates, attracting attention in many relevant fields. So far, various substantial contributions and progresses (including experimental verifications) have been made, which have provided insights on what structural and dynamical properties are needed for inducing such abrupt transformations, as well as have greatly enhanced our understanding of phase transitions in networked systems. Our intention is to offer here a monographic review on the main-stream literature, with the twofold aim of summarizing the existing results and pointing out possible directions for future research.
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Citations
Cites
Collective dynamics of ‘small-world’ networks
Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
Fortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293
Complex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010
Self-citationSynchronization in chaotic systems
Pecora, L. M., & Carroll, T. L. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.821 · Cited by 10,625
Pattern formation outside of equilibrium
Cross, M. C., & Hohenberg, P. C. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.851 · Cited by 7,859
Catastrophic cascade of failures in interdependent networks
Buldyrev, S. V., Parshani, R., Paul, G., Stanley, H. E., & Havlin, S. (2010) · Nature · doi:10.1038/nature08932 · Cited by 4,513
Synchronization in complex networks
Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.09.002 · Cited by 3,713
The Kuramoto model: A simple paradigm for synchronization phenomena
Acebrón, J. A., Bonilla, L. L., Pérez Vicente, C. J., Ritort, F., & Spigler, R. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.137 · Cited by 3,517
Interneurons of the hippocampus
Freund, T. F., & Buzsáki, G. (1998) · Hippocampus · doi:10.1002/(sici)1098-1063(1996)6:4<347::aid-hipo1>3.0.co;2-i · Cited by 3,441
The structure and dynamics of multilayer networks
Boccaletti, S., Bianconi, G., Criado, R., del Genio, C. I., Gómez-Gardeñes, J., Romance, M., Sendiña-Nadal, I., Wang, Z., & Zanin, M. (2014) · Physics Reports · doi:10.1016/j.physrep.2014.07.001 · Cited by 3,125
Self-citationNewman, M. E. J. (2003) · Physical Review E · doi:10.1103/physreve.67.026126 · Cited by 3,087
Strogatz, S. H. (2000) · Physica D: Nonlinear Phenomena · doi:10.1016/s0167-2789(00)00094-4 · Cited by 3,051
The synchronization of chaotic systems
Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., & Zhou, C. S. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00137-0 · Cited by 2,764
Self-citationPhase Synchronization of Chaotic Oscillators
Rosenblum, M. G., Pikovsky, A. S., & Kurths, J. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.1804 · Cited by 2,743
Master Stability Functions for Synchronized Coupled Systems
Pecora, L. M., & Carroll, T. L. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2109 · Cited by 2,643
Synchronization of Pulse-Coupled Biological Oscillators
Mirollo, R. E., & Strogatz, S. H. (1990) · SIAM Journal on Applied Mathematics · doi:10.1137/0150098 · Cited by 2,074
Neuronal Diversity and Temporal Dynamics: The Unity of Hippocampal Circuit Operations
Klausberger, T., & Somogyi, P. (2008) · Science · doi:10.1126/science.1149381 · Cited by 2,050
Biological rhythms and the behavior of populations of coupled oscillators
Winfree, A. T. (1967) · Journal of Theoretical Biology · doi:10.1016/0022-5193(67)90051-3 · Cited by 2,012
The world of the complex Ginzburg-Landau equation
Aranson, I. S., & Kramer, L. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.99 · Cited by 1,941
Generalized synchronization of chaos in directionally coupled chaotic systems
Rulkov, N. F., Sushchik, M. M., Tsimring, L. S., & Abarbanel, H. D. I. (1995) · Physical Review E · doi:10.1103/physreve.51.980 · Cited by 1,799
Synchronization in Small-World Systems
Barahona, M., & Pecora, L. M. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.054101 · Cited by 1,638
The role of phase synchronization in memory processes
Fell, J., & Axmacher, N. (2011) · Nature Reviews Neuroscience · doi:10.1038/nrn2979 · Cited by 1,620
Chimera States for Coupled Oscillators
Abrams, D. M., & Strogatz, S. H. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.174102 · Cited by 1,488
From Phase to Lag Synchronization in Coupled Chaotic Oscillators
Rosenblum, M. G., Pikovsky, A. S., & Kurths, J. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.4193 · Cited by 1,288
Networks formed from interdependent networks
Gao, J., Buldyrev, S. V., Stanley, H. E., & Havlin, S. (2012) · Nature Physics · doi:10.1038/nphys2180 · Cited by 1,216
Synchronization in complex networks of phase oscillators: A survey
Dörfler, F., & Bullo, F. (2014) · Automatica · doi:10.1016/j.automatica.2014.04.012 · Cited by 1,149
The Kuramoto model in complex networks
Rodrigues, F. A., Peron, T. K. D., Ji, P., & Kurths, J. (2016) · Physics Reports · doi:10.1016/j.physrep.2015.10.008 · Cited by 1,040
Kocarev, L., & Parlitz, U. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.1816 · Cited by 1,029
The asymptotic number of labeled graphs with given degree sequences
Bender, E. A., & Canfield, E. R. (1978) · Journal of Combinatorial Theory, Series A · doi:10.1016/0097-3165(78)90059-6 · Cited by 970
Low dimensional behavior of large systems of globally coupled oscillators
Ott, E., & Antonsen, T. M. (2008) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2930766 · Cited by 968
Mathematical Formulation of Multilayer Networks
De Domenico, M., Solé-Ribalta, A., Cozzo, E., Kivelä, M., Moreno, Y., Porter, M. A., Gómez, S., & Arenas, A. (2013) · Physical Review X · doi:10.1103/physrevx.3.041022 · Cited by 930
Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements
Kaneko, K. (1990) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(90)90119-a · Cited by 898
Epidemic Dynamics on an Adaptive Network
Gross, T., D’Lima, C. J. D., & Blasius, B. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.208701 · Cited by 895
Adaptive coevolutionary networks: a review
Gross, T., & Blasius, B. (2008) · Journal of The Royal Society Interface · doi:10.1098/rsif.2007.1229 · Cited by 849
Synchronization Reveals Topological Scales in Complex Networks
Arenas, A., Díaz-Guilera, A., & Pérez-Vicente, C. J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.114102 · Cited by 848
Heterogeneity in Oscillator Networks: Are Smaller Worlds Easier to Synchronize?
Nishikawa, T., Motter, A. E., Lai, Y.-C., & Hoppensteadt, F. C. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.014101 · Cited by 839
Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators
Panaggio, M. J., & Abrams, D. M. (2015) · Nonlinearity · doi:10.1088/0951-7715/28/3/r67 · Cited by 788
Parshani, R., Buldyrev, S. V., & Havlin, S. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.048701 · Cited by 788
Spontaneous synchrony in power-grid networks
Motter, A. E., Myers, S. A., Anghel, M., & Nishikawa, T. (2013) · Nature Physics · doi:10.1038/nphys2535 · Cited by 752
k-Core Organization of Complex Networks
Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.040601 · Cited by 709
Robustness of a Network of Networks
Gao, J., Buldyrev, S. V., Havlin, S., & Stanley, H. E. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.195701 · Cited by 707
Explosive Synchronization Transitions in Scale-Free Networks
Gómez-Gardeñes, J., Gómez, S., Arenas, A., & Moreno, Y. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.128701 · Cited by 674
Explosive Percolation in Random Networks
Achlioptas, D., D'Souza, R. M., & Spencer, J. (2009) · Science · doi:10.1126/science.1167782 · Cited by 673
Generalized synchronization of chaos: The auxiliary system approach
Abarbanel, H. D. I., Rulkov, N. F., & Sushchik, M. M. (1996) · Physical Review E · doi:10.1103/physreve.53.4528 · Cited by 650
Chimera states in mechanical oscillator networks
Martens, E. A., Thutupalli, S., Fourrière, A., & Hallatschek, O. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1302880110 · Cited by 633
Synchronization Transitions in a Disordered Josephson Series Array
Wiesenfeld, K., Colet, P., & Strogatz, S. H. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.404 · Cited by 627
Cluster synchronization and isolated desynchronization in complex networks with symmetries
Pecora, L. M., Sorrentino, F., Hagerstrom, A. M., Murphy, T. E., & Roy, R. (2014) · Nature Communications · doi:10.1038/ncomms5079 · Cited by 590
A Soluble Active Rotator Model Showing Phase Transitions via Mutual Entrainment
Sakaguchi, H., & Kuramoto, Y. (1986) · Progress of Theoretical Physics · doi:10.1143/ptp.76.576 · Cited by 584
Analysis of a power grid using a Kuramoto-like model
Filatrella, G., Nielsen, A. H., & Pedersen, N. F. (2008) · The European Physical Journal B · doi:10.1140/epjb/e2008-00098-8 · Cited by 574
Fast Response and Temporal Coherent Oscillations in Small-World Networks
Lago-Fernández, L. F., Huerta, R., Corbacho, F., & Sigüenza, J. A. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.2758 · Cited by 573
Bootstrap percolation on a Bethe lattice
Chalupa, J., Leath, P. L., & Reich, G. R. (1979) · Journal of Physics C: Solid State Physics · doi:10.1088/0022-3719/12/1/008 · Cited by 572
Epilepsy as a Disorder of Cortical Network Organization
Kramer, M. A., & Cash, S. S. (2012) · The Neuroscientist · doi:10.1177/1073858411422754 · Cited by 572
Stability of incoherence in a population of coupled oscillators
Strogatz, S. H., & Mirollo, R. E. (1991) · Journal of Statistical Physics · doi:10.1007/bf01029202 · Cited by 566
Network synchronization, diffusion, and the paradox of heterogeneity
Motter, A. E., Zhou, C., & Kurths, J. (2005) · Physical Review E · doi:10.1103/physreve.71.016116 · Cited by 546
Cohen, A. H., Holmes, P. J., & Rand, R. H. (1982) · Journal of Mathematical Biology · doi:10.1007/bf00276069 · Cited by 542
Synchronization in Networks of Excitatory and Inhibitory Neurons with Sparse, Random Connectivity
Börgers, C., & Kopell, N. (2003) · Neural Computation · doi:10.1162/089976603321192059 · Cited by 526
Self-Organized Synchronization in Decentralized Power Grids
Rohden, M., Sorge, A., Timme, M., & Witthaut, D. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.064101 · Cited by 519
Anticipating chaotic synchronization
Voss, H. U. (2000) · Physical Review E · doi:10.1103/physreve.61.5115 · Cited by 512
Connection graph stability method for synchronized coupled chaotic systems
Belykh, V. N., Belykh, I. V., & Hasler, M. (2004) · Physica D: Nonlinear Phenomena · doi:10.1016/j.physd.2004.03.012 · Cited by 480
Long time evolution of phase oscillator systems
Ott, E., & Antonsen, T. M. (2009) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3136851 · Cited by 463
Synchronous chaos in coupled oscillator systems
Heagy, J. F., Carroll, T. L., & Pecora, L. M. (1994) · Physical Review E · doi:10.1103/physreve.50.1874 · Cited by 462
Intracranial electroencephalographic seizure-onset patterns: effect of underlying pathology
Perucca, P., Dubeau, F., & Gotman, J. (2014) · Brain · doi:10.1093/brain/awt299 · Cited by 461
Synchronization is Enhanced in Weighted Complex Networks
Chavez, M., Hwang, D.-U., Amann, A., Hentschel, H. G. E., & Boccaletti, S. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.218701 · Cited by 460
Self-citationChang, H.-D., Chu, C.-C., & Cauley, G. (1995) · Proceedings of the IEEE · doi:10.1109/5.481632 · Cited by 459
On the stability of the Kuramoto model of coupled nonlinear oscillators
Jadbabaie, A., Motee, N., & Barahona, M. (2004) · Proceedings of the 2004 American Control Conference · doi:10.23919/acc.2004.1383983 · Cited by 451
Heil, T., Fischer, I., Elsässer, W., Mulet, J., & Mirasso, C. R. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.795 · Cited by 440
Controllability of complex networks via pinning
Sorrentino, F., di Bernardo, M., Garofalo, F., & Chen, G. (2007) · Physical Review E · doi:10.1103/physreve.75.046103 · Cited by 439
Synchronization of Bursting Neurons: What Matters in the Network Topology
Belykh, I., de Lange, E., & Hasler, M. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.188101 · Cited by 439
Recent advances in percolation theory and its applications
Saberi, A. A. (2015) · Physics Reports · doi:10.1016/j.physrep.2015.03.003 · Cited by 438
Synchronization on small-world networks
Hong, H., Choi, M. Y., & Kim, B. J. (2002) · Physical Review E · doi:10.1103/physreve.65.026139 · Cited by 438
Stochastic synchronization of oscillation in dissipative systems
Afraimovich, V. S., Verichev, N. N., & Rabinovich, M. I. (1986) · Radiophysics and Quantum Electronics · doi:10.1007/bf01034476 · Cited by 433
How dead ends undermine power grid stability
Menck, P. J., Heitzig, J., Kurths, J., & Joachim Schellnhuber, H. (2014) · Nature Communications · doi:10.1038/ncomms4969 · Cited by 430
Paths to Synchronization on Complex Networks
Gómez-Gardeñes, J., Moreno, Y., & Arenas, A. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.034101 · Cited by 422
Explosive Synchronization in Adaptive and Multilayer Networks
Zhang, X., Boccaletti, S., Guan, S., & Liu, Z. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.038701 · Cited by 419
Self-citationHong, H., & Strogatz, S. H. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.054102 · Cited by 416
Oscillation quenching mechanisms: Amplitude vs. oscillation death
Koseska, A., Volkov, E., & Kurths, J. (2013) · Physics Reports · doi:10.1016/j.physrep.2013.06.001 · Cited by 411
Dephasing and Bursting in Coupled Neural Oscillators
Han, S. K., Kurrer, C., & Kuramoto, Y. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.3190 · Cited by 408
Frequency locking in Josephson arrays: Connection with the Kuramoto model
Wiesenfeld, K. A., Colet, P., & Strogatz, S. H. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.57.1563 · Cited by 407
Spatiotemporal Intermittency in Coupled Map Lattices
Kaneko, K. (1985) · Progress of Theoretical Physics · doi:10.1143/ptp.74.1033 · Cited by 403
The role of corticothalamic coupling in human temporal lobe epilepsy
Guye, M. (2006) · Brain · doi:10.1093/brain/awl151 · Cited by 398
Avalanche Collapse of Interdependent Networks
Baxter, G. J., Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.248701 · Cited by 376
Amplitude death: The emergence of stationarity in coupled nonlinear systems
Saxena, G., Prasad, A., & Ramaswamy, R. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.09.003 · Cited by 375
Entangled Networks, Synchronization, and Optimal Network Topology
Donetti, L., Hurtado, P. I., & Muñoz, M. A. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.188701 · Cited by 346
Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays
Vicente, R., Gollo, L. L., Mirasso, C. R., Fischer, I., & Pipa, G. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0809353105 · Cited by 341
Universality in the Synchronization of Weighted Random Networks
Zhou, C., Motter, A. E., & Kurths, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.034101 · Cited by 340
Assessing seizure dynamics by analysing the correlation structure of multichannel intracranial EEG
Schindler, K., Leung, H., Elger, C. E., & Lehnertz, K. (2006) · Brain · doi:10.1093/brain/awl304 · Cited by 339
Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators
Shima, S.-I., & Kuramoto, Y. (2004) · Physical Review E · doi:10.1103/physreve.69.036213 · Cited by 336
Exact results for the Kuramoto model with a bimodal frequency distribution
Martens, E. A., Barreto, E., Strogatz, S. H., Ott, E., So, P., & Antonsen, T. M. (2009) · Physical Review E · doi:10.1103/physreve.79.026204 · Cited by 329
Distributed Delays Facilitate Amplitude Death of Coupled Oscillators
Atay, F. M. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.094101 · Cited by 320
The dynamics of chimera states in heterogeneous Kuramoto networks
Laing, C. R. (2009) · Physica D: Nonlinear Phenomena · doi:10.1016/j.physd.2009.04.012 · Cited by 320
Contrarian deterministic effects on opinion dynamics: “the hung elections scenario”
Galam, S. (2004) · Physica A: Statistical Mechanics and its Applications · doi:10.1016/j.physa.2003.10.041 · Cited by 319
Enhancing complex-network synchronization
Motter, A. E., Zhou, C. S., & Kurths, J. (2005) · Europhysics Letters (EPL) · doi:10.1209/epl/i2004-10365-4 · Cited by 317
Explosive Percolation Is Continuous
Riordan, O., & Warnke, L. (2011) · Science · doi:10.1126/science.1206241 · Cited by 316
Zero-Lag Long-Range Synchronization via Dynamical Relaying
Fischer, I., Vicente, R., Buldú, J. M., Peil, M., Mirasso, C. R., Torrent, M. C., & García-Ojalvo, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.123902 · Cited by 314
Onset of synchronization in large networks of coupled oscillators
Restrepo, J. G., Ott, E., & Hunt, B. R. (2005) · Physical Review E · doi:10.1103/physreve.71.036151 · Cited by 312
Generic behavior of master-stability functions in coupled nonlinear dynamical systems
Huang, L., Chen, Q., Lai, Y.-C., & Pecora, L. M. (2009) · Physical Review E · doi:10.1103/physreve.80.036204 · Cited by 310
Spontaneous recovery in dynamical networks
Majdandzic, A., Podobnik, B., Buldyrev, S. V., Kenett, D. Y., Havlin, S., & Eugene Stanley, H. (2014) · Nature Physics · doi:10.1038/nphys2819 · Cited by 309
Strogatz, S. H., Mirollo, R. E., & Matthews, P. C. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.2730 · Cited by 305
Critical effect of dependency groups on the function of networks
Parshani, R., Buldyrev, S. V., & Havlin, S. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1008404108 · Cited by 303
The Ehrenfest Classification of Phase Transitions: Introduction and Evolution
Jaeger, G. (1998) · Archive for History of Exact Sciences · doi:10.1007/s004070050021 · Cited by 293
Weak and strong synchronization of chaos
Pyragas, K. (1996) · Physical Review E · doi:10.1103/physreve.54.r4508 · Cited by 293
Partial synchronization in populations of pulse-coupled oscillators
Vreeswijk, C. V. (1996) · Physical Review E · doi:10.1103/physreve.54.5522 · Cited by 292
Solvable Model of Spiral Wave Chimeras
Martens, E. A., Laing, C. R., & Strogatz, S. H. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.044101 · Cited by 289
Explosive Percolation Transition is Actually Continuous
da Costa, R. A., Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.255701 · Cited by 287
Integrability of a globally coupled oscillator array
Watanabe, S., & Strogatz, S. H. (1993) · Physical Review Letters · doi:10.1103/physrevlett.70.2391 · Cited by 284
Phase synchronization effects in a lattice of nonidentical Rössler oscillators
Osipov, G. V., PIKOVSKY, A. S., Rosenblum, M. G., et al. (1997) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.55.2353 · Cited by 283
Synchronization of Kuramoto oscillators in scale-free networks
Moreno, Y., & Pacheco, A. F. (2004) · Europhysics Letters (EPL) · doi:10.1209/epl/i2004-10238-x · Cited by 281
Li, W., Bashan, A., Buldyrev, S. V., Stanley, H. E., & Havlin, S. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.228702 · Cited by 280
Dynamic Long-Term Anticipation of Chaotic States
Voss, H. U. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.014102 · Cited by 277
Remote Synchronization Reveals Network Symmetries and Functional Modules
Nicosia, V., Valencia, M., Chavez, M., Díaz-Guilera, A., & Latora, V. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.174102 · Cited by 274
Noise-Induced Phase Synchronization and Synchronization Transitions in Chaotic Oscillators
Zhou, C., & Kurths, J. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.230602 · Cited by 255
Dynamics of jamming transitions in complex networks
Echenique, P., Gómez‐Gardeñes, J., & Moreno, Y. (2005) · Europhysics Letters (EPL) · doi:10.1209/epl/i2005-10080-8 · Cited by 252
Dynamics of a large system of coupled nonlinear oscillators
Matthews, P. C., Mirollo, R. E., & Strogatz, S. H. (1991) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(91)90129-w · Cited by 246
Reshuffling scale-free networks: From random to assortative
Xulvi-Brunet, R., & Sokolov, I. M. (2004) · Physical Review E · doi:10.1103/physreve.70.066102 · Cited by 243
Thermodynamic limit of the first-order phase transition in the Kuramoto model
Pazó, D. (2005) · Physical Review E · doi:10.1103/physreve.72.046211 · Cited by 240
Detecting complex network modularity by dynamical clustering
Boccaletti, S., Ivanchenko, M., Latora, V., Pluchino, A., & Rapisarda, A. (2007) · Physical Review E · doi:10.1103/physreve.75.045102 · Cited by 237
Self-citationSpectra and eigenvectors of scale-free networks
Goh, K.-I., Kahng, B., & Kim, D. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.64.051903 · Cited by 234
Percolation in real interdependent networks
Radicchi, F. (2015) · Nature Physics · doi:10.1038/nphys3374 · Cited by 232
Chimeralike States in an Ensemble of Globally Coupled Oscillators
Yeldesbay, A., PIKOVSKY, A. S., & Rosenblum, M. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.144103 · Cited by 230
First Order Phase Transition Resulting from Finite Inertia in Coupled Oscillator Systems
Tanaka, H.-A., Lichtenberg, A. J., & Oishi, S. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.2104 · Cited by 225
Daido, H. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.1073 · Cited by 225
Frequency synchronization in a random oscillator network
Ichinomiya, T. (2004) · Physical Review E · doi:10.1103/physreve.70.026116 · Cited by 224
Synchronization in a population of globally coupled chaotic oscillators
PIKOVSKY, A. S., Rosenblum, M. G., & Kurths, J. (1996) · Europhysics Letters (EPL) · doi:10.1209/epl/i1996-00433-3 · Cited by 222
Friedman, E. B., Sun, Y., Moore, J. T., Hung, H.-T., Meng, Q. C., Perera, P., Joiner, W. J., Thomas, S. A., Eckenhoff, R. G., Sehgal, A., et al. (2010) · PLoS ONE · doi:10.1371/journal.pone.0011903 · Cited by 218
Sivaprakasam, S., Shahverdiev, E. M., Spencer, P. S. J., & Shore, K. A. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.154101 · Cited by 213
Bootstrap percolation on complex networks
Baxter, G. J., Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2010) · Physical Review E · doi:10.1103/physreve.82.011103 · Cited by 212
Impact of single links in competitive percolation
Nagler, J., Levina, A., & Timme, M. (2011) · Nature Physics · doi:10.1038/nphys1860 · Cited by 206
Strogatz, S. H., & Mirollo, R. E. (1988) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(88)90074-7 · Cited by 206
Wang, W., Kiss, I. Z., & Hudson, J. L. (2000) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.166470 · Cited by 201
Short Wavelength Bifurcations and Size Instabilities in Coupled Oscillator Systems
Heagy, J. F., Pecora, L. M., & Carroll, T. L. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4185 · Cited by 195
Chimera States: The Natural Link Between Coherence and Incoherence
Omel’chenko, O. E., MAISTRENKO, Y. L., & Tass, P. A. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.044105 · Cited by 194
Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems
Pecora, L. M. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.58.347 · Cited by 190
Daido, H. (1996) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(95)00260-x · Cited by 189
Synchronization in Complex Networks with Age Ordering
Hwang, D., Chávez, M., Amann, A., et al. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.138701 · Cited by 187
Explosive Growth in Biased Dynamic Percolation on Two-Dimensional Regular Lattice Networks
Ziff, R. M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.045701 · Cited by 183
Explosive Percolation in Scale-Free Networks
Radicchi, F., & Fortunato, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.168701 · Cited by 178
Explosive Percolation via Control of the Largest Cluster
Araújo, N. A. M., & Herrmann, H. J. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.035701 · Cited by 178
Synchronization in a pool of mutually coupled oscillators with random frequencies
Ermentrout, B. (1985) · Journal of Mathematical Biology · doi:10.1007/bf00276542 · Cited by 173
Co-evolution of Phases and Connection Strengths in a Network of Phase Oscillators
Aoki, T., & Aoyagi, T. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.034101 · Cited by 169
Synchronization of Noise-Induced Bursts in Noncoupled Sensory Neurons
Neiman, A. B., & Russell, D. F. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.138103 · Cited by 165
Cluster Explosive Synchronization in Complex Networks
Ji, P., Peron, T. K. D., Menck, P. J., Rodrigues, F. A., & Kurths, J. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.218701 · Cited by 165
The onset of jamming as the sudden emergence of an infinite k -core cluster
Schwarz, J. M., Liu, A. J., & Chayes, L. (2006) · Europhysics Letters (EPL) · doi:10.1209/epl/i2005-10421-7 · Cited by 165
Analytical and numerical studies of noise-induced synchronization of chaotic systems
Toral, R., Mirasso, C. R., Hernández-Garcı́a, E., & Piro, O. (2001) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.1386397 · Cited by 164
Kaneko, K. (1991) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(91)90103-g · Cited by 163
Lyapunov function for the Kuramoto model of nonlinearly coupled oscillators
van Hemmen, J. L., & Wreszinski, W. F. (1993) · Journal of Statistical Physics · doi:10.1007/bf01048044 · Cited by 161
Anomalous critical and supercritical phenomena in explosive percolation
D’Souza, R. M., & Nagler, J. (2015) · Nature Physics · doi:10.1038/nphys3378 · Cited by 160
Kim, M., Mashour, G. A., Moraes, S.-B., Vanini, G., Tarnal, V., Janke, E., Hudetz, A. G., & Lee, U. (2016) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2016.00001 · Cited by 160
Adaptive Synchronization of Dynamics on Evolving Complex Networks
Sorrentino, F., & Ott, E. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.114101 · Cited by 159
Simultaneous bidirectional message transmission in a chaos-based communication scheme
Vicente, R., Mirasso, C. R., & Fischer, I. (2007) · Optics Letters · doi:10.1364/ol.32.000403 · Cited by 157
Synchronization of Interconnected Networks: The Role of Connector Nodes
Aguirre, J., Sevilla-Escoboza, R., Gutiérrez, R., Papo, D., & Buldú, J. M. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.248701 · Cited by 155
Chimera states as chaotic spatiotemporal patterns
Omel’chenko, O. E., Wolfrum, M., & MAISTRENKO, Y. L. (2010) · Physical Review E · doi:10.1103/physreve.81.065201 · Cited by 154
Белых, В. Н., Belykh, I. V., & Hasler, M. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.62.6332 · Cited by 154
Daido, H. (1990) · Journal of Statistical Physics · doi:10.1007/bf01025993 · Cited by 151
Hysteretic transitions in the Kuramoto model with inertia
Olmi, S., Navas, A., Boccaletti, S., et al. (2014) · Physical Review E · doi:10.1103/physreve.90.042905 · Cited by 149
Self-citationRecent advances and open challenges in percolation
Araújo, N. A. M., Grassberger, P., Kahng, B., Schrenk, K. J., & Ziff, R. M. (2014) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2014-02266-y · Cited by 148
Kuramoto model with frequency-degree correlations on complex networks
Coutinho, B. C., Goltsev, A. V., Dorogovtsev, S. N., & Mendes, J. F. F. (2013) · Physical Review E · doi:10.1103/physreve.87.032106 · Cited by 147
Network synchronization of groups
Sorrentino, F., & Ott, E. (2007) · Physical Review E · doi:10.1103/physreve.76.056114 · Cited by 143
Construction and Analysis of Random Networks with Explosive Percolation
Friedman, E. J., & Landsberg, A. S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.255701 · Cited by 142
Bonilla, L. L., Neu, J. C., & Spigler, R. (1992) · Journal of Statistical Physics · doi:10.1007/bf01049037 · Cited by 142
Physiology of functional and effective networks in epilepsy
Yaffe, R. B., Borger, P., Mégevand, P., Groppe, D. M., Kramer, M., Chu, C. J., Santaniello, S., Meisel, C., Mehta, A. D., & Sarma, S. V. (2014) · Clinical Neurophysiology · doi:10.1016/j.clinph.2014.09.009 · Cited by 139
From scale-free to Erdos-Rényi networks
Gómez‐Gardeñes, J., & Moreno, Y. (2006) · Physical Review E · doi:10.1103/physreve.73.056124 · Cited by 134
Collective synchronisation in lattices of nonlinear oscillators with randomness
Strogatz, S. H., & Mirollo, R. E. (1988) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/21/13/005 · Cited by 133
Modular synchronization in complex networks
Oh, E., Rho, K., Hong, H., & Kahng, B. (2005) · Physical Review E · doi:10.1103/physreve.72.047101 · Cited by 132
Synchronization transition in scale-free networks: Clusters of synchrony
Lee, D. (2005) · Physical Review E · doi:10.1103/physreve.72.026208 · Cited by 131
Models for the modern power grid
Nardelli, P. H. J., Rubido, N., Wang, C., Baptista, M. S., Pomalaza‐Ráez, C., Cardieri, P., & Latva‐aho, M. (2014) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2014-02219-6 · Cited by 128
Explosive percolation: A numerical analysis
Radicchi, F., & Fortunato, S. (2010) · Physical Review E · doi:10.1103/physreve.81.036110 · Cited by 128
Self-Organized and Driven Phase Synchronization in Coupled Maps
Jalan, S., & Amritkar, R. E. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.014101 · Cited by 127
Synchronization in a system of globally coupled oscillators with time delay
Choi, M. Y., Kim, H. J., Kim, D., & Hong, H. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.61.371 · Cited by 126
Alternating Locking Ratios in Imperfect Phase Synchronization
Zaks, M. A., Park, E.-H., Rosenblum, M., et al. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.4228 · Cited by 125
Daido, H. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.231 · Cited by 124
Mechanism of Desynchronization in the Finite-Dimensional Kuramoto Model
Maistrenko, Y. L., Popovych, O. V., Burylko, O., et al. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.084102 · Cited by 123
Clustering and the synchronization of oscillator networks
McGraw, P. N., & Menzinger, M. (2005) · Physical Review E · doi:10.1103/physreve.72.015101 · Cited by 122
Impact of network topology on synchrony of oscillatory power grids
Rohden, M., Sorge, A., Witthaut, D., & Timme, M. (2014) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4865895 · Cited by 120
Core Percolation on Complex Networks
Liu, Y., Csóka, E., Zhou, H., & Pósfai, M. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.205703 · Cited by 119
Explosive synchronization in weighted complex networks
Leyva, I., Sendiña–Nadal, I., Almendral, J. A., Navas, A., Olmi, S., & Boccaletti, S. (2013) · Physical Review E · doi:10.1103/physreve.88.042808 · Cited by 117
Self-citationSynchronizability determined by coupling strengths and topology on complex networks
Gómez‐Gardeñes, J., Moreno, Y., & Arenas, À. (2007) · Physical Review E · doi:10.1103/physreve.75.066106 · Cited by 105
Complex dynamics of synergistic coinfections on realistically clustered networks
Hébert‐Dufresne, L., & Althouse, B. M. (2015) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1507820112 · Cited by 104
Spencer, J., & Wormald, N. (2007) · COMBINATORICA · doi:10.1007/s00493-007-2163-2 · Cited by 104
Ordinary percolation with discontinuous transitions
Boettcher, S., Singh, V., & Ziff, R. M. (2012) · Nature Communications · doi:10.1038/ncomms1774 · Cited by 104
Chimera states in time-varying complex networks
Buscarino, A., Frasca, M., Gambuzza, L. V., & Hövel, P. (2015) · Physical Review E · doi:10.1103/physreve.91.022817 · Cited by 104
Synchronization Interfaces and Overlapping Communities in Complex Networks
Li, D., Leyva, I., Almendral, J. A., Sendiña–Nadal, I., Buldú, J. M., Havlin, S., & Boccaletti, S. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.168701 · Cited by 104
Self-citationSynchronization in populations of globally coupled oscillators with inertial effects
Acebrón, J. A., Bonilla, L. L., & Spigler, R. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.62.3437 · Cited by 102
Synchronizing Spatiotemporal Chaos in Coupled Nonlinear Oscillators
Kocarev, L., & Parlitz, U. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.2206 · Cited by 100
Synchronization in large directed networks of coupled phase oscillators
Restrepo, J. G., Ott, E., & Hunt, B. R. (2006) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2148388 · Cited by 100
Emergence of structural patterns out of synchronization in networks with competitive interactions
Assenza, S., Gutiérrez, R., Gómez‐Gardeñes, J., Latora, V., & Boccaletti, S. (2011) · Scientific Reports · doi:10.1038/srep00099 · Cited by 98
Self-citationExplosive synchronization enhanced by time-delayed coupling
Peron, T., & Rodrigues, F. A. (2012) · Physical Review E · doi:10.1103/physreve.86.016102 · Cited by 98
Percolation Transitions Are Not Always Sharpened by Making Networks Interdependent
Son, S., Grassberger, P., & Paczuski, M. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.195702 · Cited by 96
Spontaneous emergence of contrarian-like behaviour in an opinion spreading model
Lama, M. S. D. L., López, J. M., & Wio, H. S. (2005) · Europhysics Letters (EPL) · doi:10.1209/epl/i2005-10299-3 · Cited by 94
Synchronization in complex networks with a modular structure
Park, K., Lai, Y., Gupte, S., & Kim, J. (2006) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2154881 · Cited by 92
Mesoscale and clusters of synchrony in networks of bursting neurons
Belykh, I. V., & Hasler, M. (2011) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3563581 · Cited by 91
Emerging Meso- and Macroscales from Synchronization of Adaptive Networks
Gutiérrez, R., Amann, A., Assenza, S., Gómez‐Gardeñes, J., Latora, V., & Boccaletti, S. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.234103 · Cited by 90
Self-citationBreathing synchronization in interconnected networks
Louzada, V. H. P., Araújo, N. A. M., Andrade, J. S., et al. (2013) · Scientific Reports · doi:10.1038/srep03289 · Cited by 88
Self-organized network of phase oscillators coupled by activity-dependent interactions
Aoki, T., & Aoyagi, T. (2011) · Physical Review E · doi:10.1103/physreve.84.066109 · Cited by 86
Existence of hysteresis in the Kuramoto model with bimodal frequency distributions
Pazó, D., & Montbrió, E. (2009) · Physical Review E · doi:10.1103/physreve.80.046215 · Cited by 85
Role of network topology in the synchronization of power systems
Lozano, S., Buzna, Ľ., & Díaz-Guilera, A. (2012) · The European Physical Journal B · doi:10.1140/epjb/e2012-30209-9 · Cited by 85
Exact solution for first-order synchronization transition in a generalized Kuramoto model
Hu, X. N., Boccaletti, S., Huang, W., Zhang, X., Liu, Z., Guan, S., & Lai, C.-H. (2014) · Scientific Reports · doi:10.1038/srep07262 · Cited by 83
Self-citationGeneralized coupling in the Kuramoto model
Filatrella, G., Pedersen, N. F., & Wiesenfeld, K. A. (2007) · Physical Review E · doi:10.1103/physreve.75.017201 · Cited by 83
Joiner, W. J., Friedman, E. B., Hung, H.-T., Koh, K., Sowcik, M., Sehgal, A., & Kelz, M. B. (2013) · PLoS Genetics · doi:10.1371/journal.pgen.1003605 · Cited by 82
Achlioptas process phase transitions are continuous
Riordan, O. M., & Warnke, L. (2012) · The Annals of Applied Probability · doi:10.1214/11-aap798 · Cited by 82
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Metadata
- Authors
- Boccaletti, S., Almendral, J. A., Guan, S., Leyva, I., Liu, Z., Sendiña-Nadal, I., Wang, Z., & Zou, Y.
- Venue
- Physics Reports
- Publisher
- Elsevier BV
- Published
- 2016-11
- Volume
- 660
- Pages
- 1-94
- ISSN
- 0370-1573 (ISSN-L)
- OpenAlex
- W2529489420
- Cited by
- 363
- References
- 264
- FWCI
- 16.33
- Type
- journal article
- Language
- en
- Open access
- green
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