Synchronization in complex networks
Open accessAbstract
Synchronization in complex networks Alex Arenas, 1, 2, 3 Albert D´ iaz-Guilera, 4, 2 Jurgen Kurths, 5 Yamir Moreno, 2, 6 and Changsong Zhou 7 Departament d’Enginyeria Inform` tica i Matem` tiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain a a Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Departament de F´ isica Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain Institute of Physics, University of Potsdam PF 601553, 14415 Potsdam, Germany Department of Theoretical Physics, University of Zaragoza, Zaragoza 50009, Spain Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (Dated: February 6, 2008) Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts de- voted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive nu- merical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences. PACS numbers: 05.45.Xt,89.75.Fb,89.75.Hc Contents I. Introduction II. Complex networks in a nutshell III. Coupled phase oscillator models on complex networks A. Phase oscillators 1. The Kuramoto model 2. Kuramoto model on complex networks 3. Onset of synchronization in complex networks 4. Path towards synchronization in complex networks 5. Kuramoto model on structured or modular networks 6. Synchronization by pacemakers B. Pulse-coupled models C. Coupled maps IV. Stability of the synchronized state in complex networks A. Master Stability Function formalism 1. Linear Stability and Master Stability Function 2. Measures of synchronizability 3. Synchronizability of typical network models 4. Synchronizability and structural characteristics of networks 5. Graph theoretical bounds to synchronizability 6. Synchronizability of weighted networks 7. Universal parameters controlling the synchronizability B. Design of synchronizable networks 1. Weighted couplings for enhancing synchronizability 2. Topological modification for enhancing synchronizability 3. Optimization of synchronizability C. Beyond the Master Stability Function formalism V. Applications A. Biological systems and neuroscience 1. Genetic networks 2. Circadian rhythms 3. Ecology 4. Neuronal networks 5. Cortical networks B. Computer science and engineering 1. Parallel/Distributed computation 2. Data mining 3. Consensus problems 4. Communication networks 5. Material and traffic flow 6. Power-grids C. Social sciences and economy 1. Opinion formation 2. Finance 3. World Trade Web D. Perspectives VI. Conclusions Acknowledgments References I. INTRODUCTION Synchronization, as an emerging phenomenon of a pop- ulation of dynamically interacting units, has fascinated humans from ancestral times. No matter whether the phenomenon is spontaneous or induced, synchronization captivates our minds and becomes one of the most in- teresting scientific problems. Synchronization processes are ubiquitous in nature and play a very important role in many different contexts as biology, ecology, climatol- ogy, sociology, technology, or even in arts ((Osipov et al., 2007; Pikovsky et al., 2001). It is known that synchrony
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Most climate networks assume single-variable networks, while the climate system is multivariate.
“linear correlation, 6,18 mutual information, 19 synchronization, 20 assume single-variable networks, while the climate system is a multivariate one.”
From A Big Data Guide to Understanding Climate Change: The Case for Theory-Guided Data Science (2014) · cites this paper as [20]
Cites
Collective dynamics of ‘small-world’ networks
Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060 · see citing works
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135 · see citing works
Hodgkin, A. L., & Huxley, A. F. (1952) · The Journal of Physiology · doi:10.1113/jphysiol.1952.sp004764 · Cited by 23,191 · see citing works
Statistical mechanics of complex networks
Albert, R., & Barabási, A.-L. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.47 · Cited by 20,471 · see citing works
The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719 · see citing works
Community structure in social and biological networks
Girvan, M., & Newman, M. E. J. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.122653799 · Cited by 15,502 · see citing works
Finding and evaluating community structure in networks
Newman, M. E. J., & Girvan, M. (2004) · Physical Review E · doi:10.1103/physreve.69.026113 · Cited by 13,931 · see citing works
Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
Olfati-Saber, R., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834113 · Cited by 12,788 · see citing works
Modularity and community structure in networks
Newman, M. E. J. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0601602103 · Cited by 12,256 · see citing works
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 · see citing works
Self-citationThe human brain is intrinsically organized into dynamic, anticorrelated functional networks
Fox, M. D., Snyder, A. Z., Vincent, J. L., Corbetta, M., Van Essen, D. C., & Raichle, M. E. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0504136102 · Cited by 8,553 · see citing works
Strogatz, S. H. (2001) · Nature · doi:10.1038/35065725 · Cited by 8,236 · see citing works
Distributed hierarchical processing in the primate cerebral cortex
Felleman, D. J., & Van Essen, D. C. (1991) · Cerebral Cortex · doi:10.1093/cercor/1.1.1 · Cited by 7,783 · see citing works
Chemical Oscillations, Waves, and Turbulence
Kuramoto, Y. (1984) · Springer series in synergetics · doi:10.1007/978-3-642-69689-3 · Cited by 7,242 · see citing works
Bollobás, B. (1985) · Cited by 6,196 · see citing works
Chung, F. (1996) · Regional conference series in mathematics · doi:10.1090/cbms/092 · Cited by 5,918 · see citing works
The metacommunity concept: a framework for multi‐scale community ecology
Leibold, M. A., Holyoak, M., Mouquet, N., Amarasekare, P., Chase, J. M., Hoopes, M. F., Holt, R. D., Shurin, J. B., Law, R., Tilman, D. G., et al. (2004) · Ecology Letters · doi:10.1111/j.1461-0248.2004.00608.x · Cited by 5,416 · see citing works
Erdős, P., & Rényi, A. (2022) · Publicationes Mathematicae Debrecen · doi:10.5486/pmd.1959.6.3-4.12 · Cited by 5,337 · see citing works
Cybernetics or Control and Communication in the Animal and the Machine
Wiener, N. (2019) · The MIT Press eBooks · doi:10.7551/mitpress/11810.001.0001 · Cited by 5,045 · see citing works
Assortative Mixing in Networks
Newman, M. E. J. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.208701 · Cited by 5,034 · see citing works
The Large-Scale Organization of Metabolic Networks
Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N., & Barabási, A.-L. (2000) · Nature · doi:10.1038/35036627 · Cited by 4,972 · see citing works
A synthetic oscillatory network of transcriptional regulators
Elowitz, M., & Leibler, S. (2000) · Nature · doi:10.1038/35002125 · Cited by 4,812 · see citing works
No Contagion, Only Interdependence: Measuring Stock Market Comovements
Forbes, K. J., & C, R. R. B. (2002) · The Journal of Finance · doi:10.1111/0022-1082.00494 · Cited by 4,657 · see citing works
A mechanism for cognitive dynamics: neuronal communication through neuronal coherence.
Fries, P. (2005) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2005.08.011 · Cited by 4,284 · see citing works
The architecture of complex weighted networks.
Barrat, A., Barthelemy, M., Pastor-Satorras, R., & Vespignani, A. (2003) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.0400087101 · Cited by 4,084 · see citing works
Algebraic connectivity of graphs
Fiedler, M. (1973) · Czechoslovak Mathematical Journal · doi:10.21136/cmj.1973.101168 · Cited by 4,049 · see citing works
Random graphs with arbitrary degree distributions and their applications
Newman, M. E. J., Strogatz, S. H., & Watts, D. J. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.64.026118 · Cited by 3,675 · see citing works
The Geometry of Biological Time
Winfree, A. T. (1980) · doi:10.1007/978-3-662-22492-2 · Cited by 3,613 · see citing works
Ott, E., & Wiesenfeld, K. A. (1994) · Physics Today · doi:10.1063/1.2808369 · Cited by 3,470 · see citing works
The Kuramoto model: A simple paradigm for synchronization phenomena
Acebrón, J. A., Bonilla, L. L., Vicente, C. J. P., Ritort, F., & Spigler, R. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.137 · Cited by 3,470 · see citing works
Dynamic predictions: Oscillations and synchrony in top–down processing
Engel, A. K., Fries, P., & Singer, W. (2001) · Nature Reviews Neuroscience · doi:10.1038/35094565 · Cited by 3,454 · see citing works
Preface: Cerebral Cortex Has Come of Age
Goldman, P. S., & RAKIC, P. T. (1991) · Cerebral Cortex · doi:10.1093/cercor/1.1.1-a · Cited by 3,412 · see citing works
Fractal Concepts in Surface Growth
Barabási, A.-Ĺ., Stanley, H. E., & Sander, L. M. (1995) · Physics Today · doi:10.1063/1.2808215 · Cited by 3,328 · see citing works
Dorogovtsev, S. N., & Mendes, J. F. F. (2002) · Advances In Physics · doi:10.1080/00018730110112519 · Cited by 3,231 · see citing works
Newman, M. (2002) · Physical review. E, Statistical, nonlinear, and soft matter physics · doi:10.1103/physreve.67.026126 · Cited by 3,130 · see citing works
Strogatz, S. H. (2000) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(00)00094-4 · Cited by 3,094 · see citing works
Interneurons of the neocortical inhibitory system
Markram, H., Toledo-Rodriguez, M., Wang, Y., Gupta, A., Silberberg, G., & Wu, C. (2004) · Nature Reviews Neuroscience · doi:10.1038/nrn1519 · Cited by 2,954 · see citing works
Comparing community structure identification
Danon, L., Dı́az-Guilera, A., Duch, J., & Arenas, À. (2005) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2005/09/p09008 · Cited by 2,888 · see citing works
Self-citationMaster Stability Functions for Synchronized Coupled Systems
Pecora, L. M., & Carroll, T. L. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2109 · Cited by 2,662 · see citing works
Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality
Newman, M. E. J. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.64.016132 · Cited by 2,631 · see citing works
Proceedings of the 2004 American Control Conference
(2004) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2004.1383555 · Cited by 2,605 · see citing works
Bassett, D. S., & Bullmore, E. (2006) · The Neuroscientist · doi:10.1177/1073858406293182 · Cited by 2,600 · see citing works
Characterization of complex networks: A survey of measurements
Costa, L. D. F., Rodrigues, F. A., Travieso, G., & Villas-Boas, P. R. (2007) · Advances In Physics · doi:10.1080/00018730601170527 · Cited by 2,497 · see citing works
Small worlds: the dynamics of networks between order and randomness
(2000) · Choice Reviews Online · doi:10.5860/choice.37-5722 · Cited by 2,384 · see citing works
Critical phenomena in complex networks
Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1275 · Cited by 2,220 · see citing works
Hierarchical structure in financial markets
Mantegna, R. N. (1999) · The European Physical Journal B · doi:10.1007/s100510050929 · Cited by 2,108 · see citing works
Organization, development and function of complex brain networks
SPORNS, O., CHIALVO, D., KAISER, M., & HILGETAG, C. (2004) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2004.07.008 · Cited by 2,055 · see citing works
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 2,035 · see citing works
Zwillinger, D. I. (1992) · Elsevier eBooks · doi:10.1016/b978-0-12-784391-9.50010-5 · Cited by 1,960 · see citing works
An Experimental Study of the Small World Problem
Travers, J. R., & Milgram, S. (1969) · Sociometry · doi:10.2307/2786545 · Cited by 1,884 · see citing works
Guimerà, R., Mossa, S., Turtschi, A., & Amaral, L. A. N. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0407994102 · Cited by 1,772 · see citing works
Network structure of cerebral cortex shapes functional connectivity on multiple time scales
Honey, C. J., Kötter, R., Breakspear, M. J., & Sporns, O. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0701519104 · Cited by 1,683 · see citing works
Synchronization in Small-World Systems
Barahona, M., & Pecora, L. M. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.054101 · Cited by 1,648 · see citing works
Nonequilibrium Phase Transitions in Lattice Models
Marro, J., & Dickman, R. (1999) · Cambridge University Press eBooks · doi:10.1017/cbo9780511524288 · Cited by 1,548 · see citing works
The surface statistics of a granular aggregate
Edwards, S. F., & Wilkinson, D. R. (1982) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1982.0056 · Cited by 1,539 · see citing works
Sync: The Emerging Science of Spontaneous Order
Goldenfeld, N. D. (2004) · Physics Today · doi:10.1063/1.1784276 · Cited by 1,528 · see citing works
Self-similar community structure in a network of human interactions
Guimerà, R., Danon, L., Díaz-Guilera, A., Giralt, F., & Arenas, A. (2003) · Physical Review E · doi:10.1103/physreve.68.065103 · Cited by 1,515 · see citing works
Self-citationPractical numerical algorithms for chaotic systems
(1990) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(90)90156-d · Cited by 1,506 · see citing works
Synaptic Modification by Correlated Activity: Hebb's Postulate Revisited
Bi, G., & Poo, M. (2001) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.24.1.139 · Cited by 1,476 · see citing works
Scale-Free Brain Functional Networks
Eguı́luz, V. M., Chialvo, D. R., Cecchi, G., Baliki, M. N., & Apkarian, A. V. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.018102 · Cited by 1,464 · see citing works
Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field
Stam, C. J. (2005) · Clinical Neurophysiology · doi:10.1016/j.clinph.2005.06.011 · Cited by 1,410 · see citing works
The Large‐Scale Structure of Semantic Networks: Statistical Analyses and a Model of Semantic Growth
Steyvers, M., & Tenenbaum, J. B. (2005) · Cognitive Science · doi:10.1207/s15516709cog2901_3 · Cited by 1,396 · see citing works
Detection of n : m Phase Locking from Noisy Data: Application to Magnetoencephalography
Tass, P. A., Rosenblum, M., Weule, J., Kurths, J., PIKOVSKY, A. S., Volkmann, J., Schnitzler, A., & Freund, H. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.3291 · Cited by 1,378 · see citing works
Self-citationPractical Numerical Algorithms for Chaotic Systems
Parker, T. S., & Chua, L. O. (1989) · Springer eBooks · doi:10.1007/978-1-4612-3486-9 · Cited by 1,375 · see citing works
The Small World of the Cerebral Cortex
Sporns, O., & Zwi, J. D. (2004) · Neuroinformatics · doi:10.1385/ni:2:2:145 · Cited by 1,356 · see citing works
Neurophysiological Architecture of Functional Magnetic Resonance Images of Human Brain
Salvador, R. M., John Suckling, A., Coleman, M. R., Pickard, J. D., Menon, D. K., & Bullmore, E. T. (2005) · Cerebral Cortex · doi:10.1093/cercor/bhi016 · Cited by 1,334 · see citing works
Structure of Growing Networks with Preferential Linking
Dorogovtsev, S. N., Mendes, J. F. F., & Samukhin, A. N. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.4633 · Cited by 1,320 · see citing works
Sync: The Emerging Science of Spontaneous Order
Strogatz, S. H. (2003) · Cited by 1,297 · see citing works
Universal Behavior of Load Distribution in Scale-Free Networks
Goh, K.-I., Kahng, B., & Kim, D. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.278701 · Cited by 1,246 · see citing works
Cortex: Statistics and Geometry of Neuronal Connectivity
Braitenberg, V., & Schüz, A. (1998) · doi:10.1007/978-3-662-03733-1 · Cited by 1,178 · cited 2× · see citing works
“Indeed, the wiring economy is apparent in the distributions of projection length in neural systems, which show that most neuronal projections are short [196,197].”
BackgroundModel for cascading failures in complex networks
Crucitti, P., Latora, V., & Massimo Marchiori, B. (2004) · Physical Review E · doi:10.1103/physreve.69.045104 · Cited by 1,173 · see citing works
THE LAPLACIAN SPECTRUM OF GRAPHS y
Mohar, B. (1991) · Cited by 1,119 · see citing works
The statistical analysis of the Canadian Lynx cycle.
Moran, P. (1953) · Australian Journal of Zoology · doi:10.1071/zo9530291 · Cited by 1,025 · see citing works
A Lower Bound for the Smallest Eigenvalue of the Laplacian
Cheeger, J. (2015) · Princeton University Press eBooks · doi:10.1515/9781400869312-013 · Cited by 995 · see citing works
Nagatani, T. (2002) · Reports on Progress in Physics · doi:10.1088/0034-4885/65/9/203 · Cited by 981 · see citing works
Synchronization in an array of linearly coupled dynamical systems
Wu, C. W., & Chua, L. O. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.404047 · Cited by 979 · see citing works
Complex dynamics and phase synchronization in spatially extended ecological systems
Blasius, B., Huppert, A., & Stone, L. (1999) · Nature · doi:10.1038/20676 · Cited by 970 · see citing works
Travelling waves and spatial hierarchies in measles epidemics
Grenfell, B. T., Bjørnstad, O. N., & Kappey, J. (2001) · Nature · doi:10.1038/414716a · Cited by 952 · see citing works
A Quantitative Map of the Circuit of Cat Primary Visual Cortex
Binzegger, T., Douglas, R. J., & Martin, K. A. C. (2004) · Journal of Neuroscience · doi:10.1523/jneurosci.1400-04.2004 · Cited by 879 · see citing works
Temporal structure in spatially organized neuronal ensembles: a role for interneuronal networks
Buzsáki, G., & Chrobak, J. J. (1995) · Current Opinion in Neurobiology · doi:10.1016/0959-4388(95)80012-3 · Cited by 878 · see citing works
Adaptive coevolutionary networks: a review
Gross, T., & Blasius, B. (2007) · Journal of The Royal Society Interface · doi:10.1098/rsif.2007.1229 · Cited by 862 · see citing works
Time synchronization in sensor networks: a survey
Sivrikaya, F., & Yener, B. (2004) · IEEE Network · doi:10.1109/mnet.2004.1316761 · Cited by 859 · see citing works
Synchronization Reveals Topological Scales in Complex Networks
Arenas, À., Dı́az-Guilera, A., & Vicente, C. J. P. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.114102 · Cited by 849 · see citing works
Self-citationHeterogeneity in Oscillator Networks: Are Smaller Worlds Easier to Synchronize?
Nishikawa, T., Motter, A. E., Lai, Y., & Hoppensteadt, F. C. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.014101 · Cited by 846 · see citing works
Epidemic outbreaks in complex heterogeneous networksPreprint
Moreno, Y., Pastor-satorras, R., & Vespignani, R. (2002) · Cited by 830 · see citing works
Self-citationScale-Free Networks Are Ultrasmall
Reuven Cohen, C., & Havlin, S. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.058701 · Cited by 818 · see citing works
Adaptive reconfiguration of fractal small-world human brain functional networks
Bassett, D. S., Meyer-Lindenberg, A., Achard, S., Duke, T., & Bullmore, E. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0606005103 · Cited by 814 · see citing works
Betweenness centrality in large complex networks
Barthélemy, M. (2004) · The European Physical Journal B · doi:10.1140/epjb/e2004-00111-4 · Cited by 804 · see citing works
The Dance of Life: The Other Dimension of Time
Agar, M., & Hall, E. T. (1984) · Anthropological Quarterly · doi:10.2307/3317585 · Cited by 794 · see citing works
Dynamics of market correlations: Taxonomy and portfolio analysis
Onnela, J., Chakraborti, A., Kaski, K. K., et al. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.68.056110 · Cited by 774 · see citing works
Epidemic outbreaks in complex heterogeneous networks
Moreno, Y., Pastor-Satorras, R., & Vespignani, A. (2002) · The European Physical Journal B · doi:10.1140/epjb/e20020122 · Cited by 762 · see citing works
Self-citationModel of brain rhythmic activity
Lopes, F. H. D. S., Hoeks, A. P. G., Smits, H., & Zetterberg, L. H. (1974) · Kybernetik · doi:10.1007/bf00270757 · Cited by 734 · see citing works
Ecological networks : Linking structure to dynamics in food webs
Pascual, M., & Dunne, J. A. (2006) · Cited by 715 · see citing works
Topology of the world trade web
Serrano, M. Á., & Boguñá, M. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.68.015101 · Cited by 690 · see citing works
International Symposium on Mathematical Problems in Theoretical Physics
Araki, H. (1975) · Lecture notes in physics · doi:10.1007/bfb0013294 · Cited by 675 · see citing works
Integrator or coincidence detector? The role of the cortical neuron revisited
Peter König, B., Engel, A. K., & Singer, W. (1996) · Trends in Neurosciences · doi:10.1016/s0166-2236(96)80019-1 · Cited by 674 · see citing works
Cybernetics-or control and communication in the animal and the machine
Charp, S. (1949) · Journal of the Franklin Institute · doi:10.1016/0016-0032(49)90745-0 · Cited by 672 · see citing works
Hippocampal CA1 interneurons: an in vivo intracellular labeling study
Sik, A., Penttonen, M., Ylinen, A., & Buzsaki, G. (1995) · The Journal of Neuroscience · doi:10.1523/jneurosci.15-10-06651.1995 · Cited by 669 · see citing works
Kaiser, M., & Hilgetag, C. C. (2006) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0020095 · Cited by 638 · see citing works
Small Worlds: The Dynamics of Networks between Order and Randomness
Watts, D. J., & Bak, P. (2000) · Physics Today · doi:10.1063/1.1333299 · Cited by 602 · see citing works
Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing
García‐Ojalvo, J., Elowitz, M. B., & Strogatz, S. H. (2004) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0307095101 · Cited by 592 · see citing works
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 576 · see citing works
Fast Response and Temporal Coherent Oscillations in Small-World Networks
Lago-Fernández, L. F., Huerta, R., Corbacho, F., & Siguenza, J. A. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.2758 · Cited by 572 · see citing works
Analysis of the structure of complex networks at different resolution levels
Arenas, À., Fernández, A., & Gómez, S. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/5/053039 · Cited by 550 · see citing works
Stam, C. J. (2003) · Neuroscience Letters · doi:10.1016/j.neulet.2003.10.063 · Cited by 550 · see citing works
Hilgetag, C. C., Burns, G., O’Neill, M. A., Scannell, J. W., & Young, M. P. (2000) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2000.0551 · Cited by 548 · see citing works
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 547 · see citing works
Self-citationDorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2002) · Physical Review E · doi:10.1103/physreve.65.066122 · Cited by 540 · see citing works
The application of graph theoretical analysis to complex networks in the brain
Reijneveld, J. C., Ponten, S. C., Berendse, H. W., & Stam, C. J. (2007) · Clinical Neurophysiology · doi:10.1016/j.clinph.2007.08.010 · Cited by 523 · see citing works
Graph theory, combinatorics, and applications
Alavi, Y., Chartrand, G., & Oellermann, O. R. (2017) · Cited by 520 · see citing works
Spectra of random graphs with given expected degrees
Chung, F., Lü, L., & Vu, V. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0937490100 · Cited by 505 · see citing works
Hierarchical Organization Unveiled by Functional Connectivity in Complex Brain Networks
Zhou, C., Zemanová, L., Zamora‐López, G., Hilgetag, C. C., & Kurths, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.238103 · Cited by 504 · see citing works
Self-citationWiring Optimization in Cortical Circuits
Chklovskii, D. B., Schikorski, T., & Stevens, C. F. (2002) · Neuron · doi:10.1016/s0896-6273(02)00679-7 · Cited by 499 · see citing works
Structure and evolution of the world trade network
Garlaschelli, D., & Loffredo, M. I. (2005) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.02.075 · Cited by 496 · see citing works
Eigenvalues of the Laplacian of a graph ∗
Anderson, W. N., & Morley, T. D. (1985) · Linear and Multilinear Algebra · doi:10.1080/03081088508817681 · Cited by 486 · see citing works
Interneuron Diversity series: Circuit complexity and axon wiring economy of cortical interneurons
Buzsáki, G., Geisler, C. E., Henze, D. A., & Wang, X. (2004) · Trends in Neurosciences · doi:10.1016/j.tins.2004.02.007 · Cited by 483 · see citing works
Synchronization in Oscillatory Networks
Osipov, G. V., Kurths, J., & Zhou, C. (2007) · Springer series in synergetics · doi:10.1007/978-3-540-71269-5 · Cited by 476 · see citing works
Self-citationA topological analysis of the Italian electric power grid
Crucitti, P., Latora, V., & Massimo Marchiori, B. (2004) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2004.02.029 · Cited by 474 · see citing works
Connection graph stability method for synchronized coupled chaotic systems
Белых, В. Н., Belykh, I. V., & Hasler, M. (2004) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2004.03.012 · Cited by 474 · see citing works
Patterns of Link Reciprocity in Directed Networks
Garlaschelli, D., & Loffredo, M. I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.268701 · Cited by 467 · see citing works
Yook, S., Jeong, H., Barabási, A.-Ĺ., & Tu, Y. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5835 · Cited by 467 · see citing works
Synchronization is Enhanced in Weighted Complex Networks
Chávez, M., Hwang, D., Amann, A., Hentschel, H. G. E., & Boccaletti, S. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.218701 · Cited by 462 · see citing works
Synchronization on small-world networks
Hong, H., Choi, M. Y., & Kim, B. J. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.026139 · Cited by 441 · see citing works
SPECTRAL GRAPH THEORY (CBMS Regional Conference Series in Mathematics 92)
Biggs, N. (1998) · Bulletin of the London Mathematical Society · doi:10.1112/s0024609397223611 · Cited by 437 · see citing works
Paths to Synchronization on Complex Networks
Gómez‐Gardeñes, J., Moreno, Y., & Arenas, À. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.034101 · Cited by 422 · see citing works
Self-citationMean-Field Solution of the Small-World Network Model
Newman, M. E. J., Moore, C., & Watts, D. J. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.3201 · Cited by 412 · see citing works
Trade intensity and business cycle synchronization: Are developing countries any different?
Calderon, C. A., Chong, A. E., & Stein, E. H. (2006) · Journal of International Economics · doi:10.1016/j.jinteco.2006.06.001 · Cited by 406 · see citing works
Dynamical Weights and Enhanced Synchronization in Adaptive Complex Networks
Zhou, C., & Kurths, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.164102 · Cited by 398 · see citing works
Self-citationAndrade, J. S., Herrmann, H. J., Andrade, R. F. S., & da Silva, L. R. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.018702 · Cited by 398 · see citing works
The Dance of Life: The Other Dimension of Time
Dennis, P. A., & Hall, E. T. (1984) · Ethnohistory · doi:10.2307/482722 · Cited by 398 · see citing works
Ultrafast consensus in small-world networks
Olfati‐Saber, R. (2005) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2005.1470321 · Cited by 390 · see citing works
The Network Structure of Food Webs
Dunne, J. A. (2005) · doi:10.1093/oso/9780195188165.003.0002 · Cited by 374 · see citing works
The Connectional Organization of the Cortico-thalamic System of the Cat
Scannell, J. W. (1999) · Cerebral Cortex · doi:10.1093/cercor/9.3.277 · Cited by 371 · see citing works
Blinking model and synchronization in small-world networks with a time-varying coupling
Belykh, I. V., Белых, В. Н., & Hasler, M. (2004) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2004.03.013 · Cited by 359 · see citing works
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 347 · see citing works
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 342 · see citing works
Self-citationGlobal synchronization and asymptotic stability of complex dynamical networks
Li, Z. Z., & Chen, G. (2006) · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · doi:10.1109/tcsii.2005.854315 · Cited by 341 · see citing works
Isoperimetric numbers of graphs
Mohar, B. (1989) · Journal of Combinatorial Theory Series B · doi:10.1016/0095-8956(89)90029-4 · Cited by 335 · see citing works
Earn, D. J. D., Levin, S. A., & Rohani, P. (2000) · Science · doi:10.1126/science.290.5495.1360 · Cited by 329 · see citing works
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 324 · see citing works
Self-citationEigenvalue Spectra of Random Matrices for Neural Networks
Rajan, K., & Abbott, L. F. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.188104 · Cited by 320 · see citing works
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 · see citing works
Eigenvalues, diameter, and mean distance in graphs
Mohar, B. (1991) · Graphs and Combinatorics · doi:10.1007/bf01789463 · Cited by 306 · see citing works
Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint
Li, X., & Chen, G. (2003) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2003.818611 · Cited by 306 · see citing works
Self-Sustained Activity in a Small-World Network of Excitable Neurons
Roxin, A., Riecke, H., & Solla, S. A. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.198101 · Cited by 303 · see citing works
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 283 · see citing works
Self-citationDorogovtsev, S. N., Goltsev, A. V., Mendes, J. F. F., & Samukhin, A. N. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.68.046109 · Cited by 281 · see citing works
Spectral properties and synchronization in coupled map lattices
Jost, J., & Joy, M. P. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.016201 · Cited by 278 · see citing works
Enhancing complex-network synchronization
Motter, A. E., Zhou, C., & Kurths, J. (2005) · Cited by 277 · see citing works
Self-citationDelays, Connection Topology, and Synchronization of Coupled Chaotic Maps
Atay, F. M., Jost, J., & Wende, A. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.144101 · Cited by 276 · see citing works
Computational analysis of functional connectivity between areas of primate cerebral cortex
Stephan, K. E., Hilgetag, C. C., Burns, G., O’Neill, M. A., Young, M. P., & Kötter, R. (2000) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2000.0552 · Cited by 269 · see citing works
Synchronization is optimal in nondiagonalizable networks
Nishikawa, T., & Motter, A. E. (2006) · Physical Review E · doi:10.1103/physreve.73.065106 · Cited by 263 · see citing works
Characterizing the Dynamical Importance of Network Nodes and Links
Restrepo, J. G., Ott, E., & Hunt, B. R. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.094102 · Cited by 262 · see citing works
Evaluating North American electric grid reliability using the Barabási–Albert network model
Chassin, D. P., & Posse, C. (2005) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.02.051 · Cited by 253 · see citing works
Complexity and synchronization of the World trade Web
Li, X., Jin, Y., & Chen, G. (2003) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(03)00567-3 · Cited by 253 · see citing works
Clustered Organization of Cortical Connectivity
Hilgetag, C. C., & Kaiser, M. (2004) · Neuroinformatics · doi:10.1385/ni:2:3:353 · Cited by 251 · see citing works
Host immunity and synchronized epidemics of syphilis across the United States
Grassly, N. C., Fraser, C., & Garnett, G. P. (2005) · Nature · doi:10.1038/nature03072 · Cited by 249 · see citing works
Disturbances in a power transmission system
Sachtjen, M. L., Carreras, B. A., & Lynch, V. E. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.61.4877 · Cited by 245 · see citing works
Factors that predict better synchronizability on complex networks
Hong, H., Kim, B. J., Choi, M. Y., & Park, H. (2004) · Physical Review E · doi:10.1103/physreve.69.067105 · Cited by 244 · see citing works
Common Dynamic Structure of Canada Lynx Populations Within Three Climatic Regions
Stenseth, N. C., Chan, K., Tong, H., et al. (1999) · Science · doi:10.1126/science.285.5430.1071 · Cited by 237 · see citing works
Synchronous chaos in coupled map lattices with small-world interactions
Gade, P. M., & Hu, C. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.62.6409 · Cited by 233 · see citing works
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 232 · see citing works
Frequency synchronization in a random oscillator network
Ichinomiya, T. (2004) · Physical Review E · doi:10.1103/physreve.70.026116 · Cited by 228 · see citing works
Fractal concepts in surface growth
Family, F. (1996) · Journal of Statistical Physics · doi:10.1007/bf02179563 · Cited by 207 · see citing works
Degesys, J., Rose, I., Patel, A. D., et al. (2007) · doi:10.1145/1236360.1236363 · Cited by 206 · see citing works
Diffusion, localization and dispersion relations on “small-world” lattices
Monasson, R. (1999) · The European Physical Journal B · doi:10.1007/s100510051038 · Cited by 205 · see citing works
Inhibitory CA1-CA3-Hilar Region Feedback in the Hippocampus
Attila Gabor, S. I. K., Ylinen, A., Penttonen, M., & Buzsáki, G. (1994) · Science · doi:10.1126/science.8085161 · Cited by 197 · see citing works
Garey, L. J. (1999) · Journal of Anatomy · doi:10.1046/j.1469-7580.1999.194101535.x · Cited by 189 · see citing works
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 · see citing works
Optimal Paths in Disordered Complex Networks
Braunstein, L. A., Buldyrev, S. V., Reuven Cohen, C., Havlin, S., & Stanley, E. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.168701 · Cited by 187 · see citing works
Fink, K. S., Johnson, G., Carroll, T., Mar, D., & Pecora, L. M. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.61.5080 · Cited by 177 · see citing works
Structure–function relationship in complex brain networks expressed by hierarchical synchronization
Zhou, C., Zemanová, L., Zamora‐López, G., Hilgetag, C. C., & Kurths, J. (2007) · New Journal of Physics · doi:10.1088/1367-2630/9/6/178 · Cited by 171 · see citing works
Self-citationNon-linear dynamics of cardiac excitation and impulse propagation
Chialvo, D. R., & Jalife, J. (1987) · Nature · doi:10.1038/330749a0 · Cited by 170 · see citing works
The Number of Synaptic Inputs and the Synchrony of Large, Sparse Neuronal Networks
Golomb, D., & Hansel, D. (2000) · Neural Computation · doi:10.1162/089976600300015529 · Cited by 169 · see citing works
Control of Neuronal Synchrony by Nonlinear Delayed Feedback
Popovych, O. V., Hauptmann, C., & Tass, P. A. (2006) · Biological Cybernetics · doi:10.1007/s00422-006-0066-8 · Cited by 168 · see citing works
Synchronization processes in complex networks
Arenas, À., Dı́az-Guilera, A., & Vicente, C. J. P. (2006) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2006.09.029 · Cited by 160 · see citing works
Self-citationAdaptive Synchronization of Dynamics on Evolving Complex Networks
Sorrentino, F., & Ott, E. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.114101 · Cited by 159 · see citing works
Ad-hoc Networks: Fundamental Properties and Network Topologies
Hekmat, R. (2006) · Springer eBooks · doi:10.1007/1-4020-5166-2 · Cited by 156 · see citing works
Maximum performance at minimum cost in network synchronization
Nishikawa, T., & Motter, A. E. (2006) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2006.09.007 · Cited by 152 · see citing works
Nicol, D., & Fujimoto, R. (1994) · Annals of Operations Research · doi:10.1007/bf02136831 · Cited by 150 · see citing works
Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
Ariaratnam, J. T., & Strogatz, S. H. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.4278 · Cited by 147 · see citing works
Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations
Korniss, G., Novotny, M. A., Guclu, H., et al. (2003) · Science · doi:10.1126/science.1079382 · Cited by 144 · see citing works
Synaptic pathways in neural microcircuits
Silberberg, G., Grillner, S. E., LeBeau, F. E. N., Maex, R., & Markram, H. (2005) · Trends in Neurosciences · doi:10.1016/j.tins.2005.08.004 · Cited by 144 · see citing works
Abnormal Synchronization in Complex Clustered Networks
Huang, L., Park, K., Lai, Y., et al. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.164101 · Cited by 142 · see citing works
Hierarchical synchronization in complex networks with heterogeneous degrees
Zhou, C., & Kurths, J. (2006) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2150381 · Cited by 139 · see citing works
Self-citationSpontaneous Structure Formation in a Network of Chaotic Units with Variable Connection Strengths
Ito, J., & Kaneko, K. (2001) · Physical Review Letters · doi:10.1103/physrevlett.88.028701 · Cited by 137 · see citing works
Random Delays and the Synchronization of Chaotic Maps
Masoller, C., & Martı́, A. C. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.134102 · Cited by 136 · see citing works
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 · see citing works
Self-citationModular synchronization in complex networks
Oh, E., Rho, K., Hong, H., & Kahng, B. (2005) · Physical Review E · doi:10.1103/physreve.72.047101 · Cited by 134 · see citing works
Interplay between topology and dynamics in the World Trade Web
Garlaschelli, D., Matteo, T. D., Aste, T., et al. (2007) · The European Physical Journal B · doi:10.1140/epjb/e2007-00131-6 · Cited by 133 · see citing works
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 · see citing works
Synchronization transition in scale-free networks: Clusters of synchrony
Lee, D. (2005) · Physical Review E · doi:10.1103/physreve.72.026208 · Cited by 131 · see citing works
Structural and functional clusters of complex brain networks
Zemanová, L., Zhou, C., & Kurths, J. (2006) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2006.09.008 · Cited by 128 · see citing works
Self-citationSelf-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 · see citing works
Performance of networks of artificial neurons: The role of clustering
Kim, B. J. (2004) · Physical Review E · doi:10.1103/physreve.69.045101 · Cited by 126 · see citing works
Motif-based communities in complex networks
Arenas, À., Fernández, A., Fortunato, S., & Gómez, S. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/22/224001 · Cited by 124 · see citing works
CHANGING OPINIONS IN A CHANGING WORLD: A NEW PERSPECTIVE IN SOCIOPHYSICS
Pluchino, A., Latora, V., & Rapisarda, A. (2005) · International Journal of Modern Physics C · doi:10.1142/s0129183105007261 · Cited by 123 · see citing works
Minimum spanning trees of weighted scale-free networks
Macdonald, P. J., Almaas, E., & Barabási, A.-Ĺ. (2005) · Europhysics Letters (EPL) · doi:10.1209/epl/i2005-10232-x · Cited by 122 · see citing works
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 · see citing works
Local Structure of Directed Networks
Bianconi, G., Gulbahce, N., & Motter, A. E. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.118701 · Cited by 121 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
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 · see citing works
Diffusion Dynamics on Multiplex Networks
Gómez, S., Díaz-Guilera, A., Gómez-Gardeñes, J., Pérez-Vicente, C. J., Moreno, Y., & Arenas, A. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.028701 · Cited by 1,003 · see citing works
Self-citationRobust detection of dynamic community structure in networks
Bassett, D. S., Porter, M. A., Wymbs, N. F., Grafton, S. T., Carlson, J. M., & Mucha, P. J. (2013) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4790830 · Cited by 425 · see citing works
The backbone of the climate network
Donges, J. F., Zou, Y., Marwan, N., & Kurths, J. (2009) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/87/48007 · Cited by 473 · see citing works
Self-citationQuantification of network structural dissimilarities
Schieber, T. A., Carpi, L., Díaz-Guilera, A., Pardalos, P. M., Masoller, C., & Ravetti, M. G. (2017) · Nature Communications · doi:10.1038/ncomms13928 · Cited by 237 · see citing works
Self-citationA Big Data Guide to Understanding Climate Change: The Case for Theory-Guided Data Science
Faghmous, J. H., & Kumar, V. (2014) · Big Data · doi:10.1089/big.2014.0026 · Cited by 223 · see citing works
Quantum Navigation and Ranking in Complex Networks
Sánchez-Burillo, E., Duch, J., Gómez-Gardeñes, J., & Zueco, D. (2012) · Scientific Reports · doi:10.1038/srep00605 · Cited by 115 · see citing works
- Authors
- Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C.
- Affiliations
- Universidad de Zaragoza (ES)
- Hong Kong Baptist University (HK)
- Corresponding author
- Moreno, Yamir
- Venue
- Physics Reports
- Publisher
- Elsevier BV
- Published
- 2008-12
- Volume
- 469
- Issue
- 3
- Pages
- 93-153
- ISSN
- 0370-1573 (ISSN-L)
- OpenAlex
- W261461018
- Semantic Scholar
- fde7fb9ea93da064dc18ab32ecd1b647dd58705e
- Cited by
- 3,713
- References
- 294
- Citations by year
- 2026: 202 · 2025: 200 · 2024: 196 · 2023: 204 · 2022: 199 · 2021: 250 · 2020: 195 · 2019: 231 · 2018: 237 · 2017: 215 · 2016: 230 · 2015: 241 · 2014: 238 · 2013: 256 · 2012: 210
- FWCI
- 221.94
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physics Reports (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- University of North Texas Digital Library (University of North Texas) (submittedVersion)
- eScholarship (California Digital Library) (submittedVersion)
- Publication Database PIK (Potsdam Institute for Climate Impact Research (PIK)) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Physical Sciences › Computer Science › Computer Networks and Communications › Neural Networks Stability and Synchronization
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Keywords
- synchronization, complex networks, coupled oscillators, network topology, structure-function relationship, biological systems, engineering applications, social networks, economic applications
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
