## Influence of Network Topology on Synchronization

*30 Aug 2021 10:40*

Yet Another Inadequate Placeholder, last seriously updated 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; Synchronization; Parallel and Distributed Computing

- 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

- "Synchronization Reveals Topological Scales in Complex
Networks",
Physical Review
Letters
- 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

- "Clustering and
Synchronization of Oscillator Networks", cond-mat/0501663 = Physical Review
E
- 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