Influence of Network Topology on Synchronization

Last update: 12 Apr 2025 11:12
First version: 12 October 2006

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Yet Another Inadequate Placeholder, last seriously updated when created in 2006 (around which time I actually read many of the papers I list as "To read" below, but I cannot now [2021] remember which...)

Are certain kinds of networks always easier to synchronize? Or generically easier to synchronize, for very broad classes of dynamics? Does it matter if the couplings are heterogeneous? Does it matter if the nodes are heterogeneous? Are there perhaps local aspects which make parts of networks easier to synchronize, or apt to synchronize?

See also:
• Complex Networks
• Economic Networks
• Parallel and Distributed Computing
• Synchronization

Recommended:
• Fatihcan M. Atay, Türker Biyikoglu and Jürgen Jost, "On the synchronization of networks with prescribed degree distributions", nlin.AO/0407024 [Networks with any degree distribution can be made arbitrarily hard to synchronize]
• Fatihcan M. Atay, Jürgen Jost and Andreas Wende, "Delays, connection topology, and synchronization of coupled chaotic maps", cond-mat/0312177

To read:
• O. Alvarez-Llamoza, K. Tucci, M. G. Cosenza, and M. Pineda, "Random global coupling induces synchronization and nontrivial collective behavior in networks of chaotic maps", nlin.CD/0612010
• Alex Arenas, Albert Diaz-Guilera, Jurgen Kurths, Yamir Moreno, Changsong Zhou, "Synchronization in complex networks", Physics Reports 469 (2008): 93--153, arxiv:0805.2976
• Alex Arenas, Albert Diaz-Guilera and Conrad J. Perez-Vicente
  • "Synchronization Reveals Topological Scales in Complex Networks", Physical Review Letters 96 (2006): 114102 = cond-mat/0511730
  • "Synchronization processes in complex networks", nlin.AO/0610057
• Fatihcan M. Atay and Turker Biyikoglu, "Graph operations and synchronization of complex networks", Physical Review E 72 (2005): 016217
• Fatihcan M. Atay, Turker Biyikoglu and Juergen Jost, "Network synchronization: Spectral versus statistical properties", arxiv:0706.3069 = Physica D 224 (2006):35--41
• Mauricio Barahona and Louis M. Pecora, "Synchronization in small-world systems," nlin.CD/0112023
• Mario di Bernardo, Franco Garofalo and Francesco Sorrentino, "Synchronization of degree correlated physical networks", cond-mat/0506236
• Luca Donetti, Pablo I. Hurtado, and Miguel A. Munoz, "Synchronization in Network Structures: Entangled Topology as Optimal Architecture for Network Design", cond-mat/0602351
• Prashant M. Gade and Sudeshna Sinha, "How Crucial Is Small World Connectivity for Dynamics?", International Journal of Bifurcation and Chaos 16 (2006): 2767--2775
• Jesus Gomez-Gardenes, Yamir Moreno, Alex Arenas, "Paths to Synchronization on Complex Networks", cond-mat/0608314
• Carsten Grabow, Steven Hill, Stefan Grosskinsky, Marc Timme, "Do Small Worlds Synchronize Fastest?", arxiv:1005.3757
• H. Guclu, G. Korniss, M. A. Novotny, Z. Toroczkai and Z. R´cz, "Synchronization landscapes in small-world-connected computer networks", Physical Review E 73 (2006): 066115 = cond-mat/0601058
• H. Hong, M. Y. Choi, and Beom Jun Kim, "Synchronization on small-world networks," cond-mat/0110359
• Sarika Jalan and R. E. Amritkar, "Self-organized and driven phase synchronization in coupled map scale free networks," nlin.AO/0201051
• Jürgen Jost and M. P. Joy, "Spectral Properties and Synchronization in Coupled Map Lattices," Physical Review E 65 (2002): 016201 = nlin.CD/0110037
• Deok-Sun Lee, "Synchronization transition in scale-free networks: clusters of synchrony", cond-mat/0410635
• Kristina Lerman, Rumi Ghosh, "Network Structure, Topology and Dynamics in Generalized Models of Synchronization", Physical Review E 86 (2012): 026108, arxiv:1203.1338
• Ivano Lodato, Stefano Boccaletti and Vito Latora, "Synchronization Properties of Network Motifs", physics/0609126
• Wenlian Lu, Fatihcan M. Atay, Jürgen Jost, "Chaos synchronization in networks of coupled maps with time-varying topologies", European Physical Journal B 63 (2008): 399--406, arxiv:0812.2648
• M. S. O. Massunaga and M. Bahiana, "Synchronization in large populations of limit cycle oscillators with long-range interactions," cond-mat/0201508
• Manuel A. Matias, "Synchronization in Complex Networks: a Comment on two recent PRL papers", cond-mat/0507471
• Patrick N. McGraw and Michael Menzinger
  • "Clustering and Synchronization of Oscillator Networks", cond-mat/0501663 = Physical Review E 72 (2005): 015101 ["in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization"]
  • "Laplacian Spectra as a Diagnostic Tool for Network Structure and Dynamics", Physical Review E 77 (2010): 031102, arxiv:0708.4206
• Yamir Moreno and Amalio E. Pacheco, "Synchronization of Phase Oscillators in Scale-Free Networks", cond-mat/0401266
• Adilson E. Motter, Changsong Zhou and Juergen Kurths, "Enhancing complex-network synchronization", cond-mat/0406207
• Takashi Nishikawa, Adilson E. Motter, Ying-Cheng Lai and Frank C. Hoppensteadt, "Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?" cond-mat/0306625
• E. Oh, K. Rho, H. Hong and B. Kahng, "Modular synchronization in complex networks", cond-mat/0408202
• Tiago Pereira, "Hub Synchronization in Scale-Free Networks", arxiv:1005.3803
• Juan G. Restrepo, Edward Ott and Brian R. Hunt
  • "Spatial Patterns of Desynchronization Bursts in Networks", nlin.CD/0401007
  • "Emergence of Coherence in Complex Networks of Heterogeneous Dynamical Systems", Physical Review Letters 96 (2006): 254103 = cond-mat/0601639
• Srinivas Gorur Shandilya and Marc Timme, "Inferring Network Topology from Complex Dynamics", arxiv:1007.1640
• Marc Timme, "Revealing Network Connectivity From Dynamics", cond-mat/0610188