http://bactra.org/notebooks Cosma's Notebooks en http://bactra.org/notebooks/2007/09/01#topology-and-synchronization <P>Are certain kinds of networks <em>always</em> easier to synchronize? Or <em>generically</em> 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 <em>local</em> aspects which make <em>parts</em> of networks easier to synchronize, or apt to synchronize? <P>See also: <a href="complex-networks.html">Complex Networks</a>; <a href="synchronization.html">Synchronization</a> <ul>Recommended: <li>Fatihcan M. Atay, T&uuml;rker Biyikoglu and J&uuml;rgen Jost, "On the synchronization of networks with prescribed degree distributions", <a href="http://arxiv.org/abs/nlin.AO/0407024">nlin.AO/0407024</a> [Networks with any degree distribution can be made arbitrarily hard to synchronize] <li>Fatihcan M. Atay, J&uuml;rgen Jost and Andreas Wende, "Delays, connection topology, and synchronization of coupled chaotic maps", <a href="http://arxiv.org/abs/cond-mat/0312177">cond-mat/0312177</a> </ul> <ul>To read: <li>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", <a href="http://arxiv.org/abs/nlin.CD/0612010">nlin.CD/0612010</a> <li>Alex Arenas, Albert Diaz-Guilera and Conrad J. Perez-Vicente <ul> <li>"Synchronization Reveals Topological Scales in Complex Networks", <a href="http://dx.doi.org/10.1103/PhysRevLett.96.114102"><cite>Physical Review Letters</cite> <strong>96</strong> (2006): 114102</a> = <a href="http://arxiv.org/abs/cond-mat/0511730">cond-mat/0511730</a> <li>"Synchronization processes in complex networks", <a href="http://arxiv.org/abs/nlin.AO/0610057">nlin.AO/0610057</a> </ul> <li>Fatihcan M. Atay and Turker Biyikoglu, "Graph operations and synchronization of complex networks", <a href="http://dx.doi.org/10.1103/PhysRevE.72.016217"><cite>Physical Review E</cite> <strong>72</strong> (2005): 016217</a> <li>Fatihcan M. Atay, Turker Biyikoglu and Juergen Jost, "Network synchronization: Spectral versus statistical properties", <a href="http://arxiv.org/abs/0706.3069">arxiv:0706.3069</a> = <cite>Physica D</cite> <strong>224</strong> (2006):35--41 <li>Mauricio Barahona and Louis M. Pecora, "Synchronization in small-world systems," <a href="http://arxiv.org/abs/nlin.CD/0112023">nlin.CD/0112023</a> <li>Mario di Bernardo, Franco Garofalo and Francesco Sorrentino, "Synchronization of degree correlated physical networks", <a href="http://arxiv.org/abs/cond-mat/0506236">cond-mat/0506236</a> <li>Luca Donetti, Pablo I. Hurtado, and Miguel A. Munoz, "Synchronization in Network Structures: Entangled Topology as Optimal Architecture for Network Design", <a href="http://arxiv.org/abs/cond-mat/0602351">cond-mat/0602351</a> <li>Prashant M. Gade and Sudeshna Sinha, "How Crucial Is Small World Connectivity for Dynamics?", <a href="http://dx.doi.org/10.1142/S0218127406016458"><cite>International Journal of Bifurcation and Chaos</cite> <strong>16</strong> (2006): 2767--2775</a> <li>Jesus Gomez-Gardenes, Yamir Moreno, Alex Arenas, "Paths to Synchronization on Complex Networks", <a href="http://arxiv.org/abs/cond-mat/0608314">cond-mat/0608314</a> <li>H. Guclu, G. Korniss, M. A. Novotny, Z. Toroczkai and Z. R&acute;cz, "Synchronization landscapes in small-world-connected computer networks", <a href="http://dx.doi.org/10.1103/PhysRevE.73.066115"><cite>Physical Review E</cite> <strong>73</strong> (2006): 066115</a> = <a href="http://arxiv.org/abs/cond-mat/0601058">cond-mat/0601058</a> <li>H. Hong, M. Y. Choi, and Beom Jun Kim, "Synchronization on small-world networks," <a href="http://arxiv.org/abs/cond-mat/0110359">cond-mat/0110359</a> <li>Sarika Jalan and R. E. Amritkar, "Self-organized and driven phase synchronization in coupled map scale free networks," <a href="http://arxiv.org/abs/nlin.AO/0201051">nlin.AO/0201051</a> <li>J&uuml;rgen Jost and M. P. Joy, "Spectral Properties and Synchronization in Coupled Map Lattices," <citE>Physical Review E</cite> <strong>65</strong> (2002): 016201 = <a href="http://arxiv.org/abs/nlin.CD/0110037">nlin.CD/0110037</a> <li>Deok-Sun Lee, "Synchronization transition in scale-free networks: clusters of synchrony", <a href="http://arxiv.org/abs/cond-mat/0410635">cond-mat/0410635</a> <li>Ivano Lodato, Stefano Boccaletti and Vito Latora, "Synchronization Properties of Network Motifs", <a href="http://arxiv.org/abs/physics/0609126">physics/0609126</a> <li>M. S. O. Massunaga and M. Bahiana, "Synchronization in large populations of limit cycle oscillators with long-range interactions," <a href="http://arxiv.org/abs/cond-mat/0201508">cond-mat/0201508</a> <li>Manuel A. Matias, "Synchronization in Complex Networks: a Comment on two recent PRL papers", <a href="http://arxiv.org/abs/cond-mat/0507471">cond-mat/0507471</a> <li>Patrick N. McGraw and Michael Menzinger <ul> <li>"Clustering and Synchronization of Oscillator Networks", <a href="http://arxiv.org/abs/cond-mat/0501663">cond-mat/0501663</a> = <a href="http://dx.doi.org/10.1103/PhysRevE.72.015101"><cite>Physical Review E</cite> <strong>72</strong> (2005): 015101</a> ["in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization"] <li>"Laplacian Spectra as a Diagnostic Tool for Network Structure and Dynamics", <a href="http://arxiv.org/abs/0708.4206">arxiv:0708.4206</a> </ul> <li>Yamir Moreno and Amalio E. Pacheco, "Synchronization of Phase Oscillators in Scale-Free Networks", <a href="http://arxiv.org/abs/cond-mat/0401266">cond-mat/0401266</a> <li>Adilson E. Motter, Changsong Zhou and Juergen Kurths, "Enhancing complex-network synchronization", <a href="http://arxiv.org/abs/cond-mat/0406207">cond-mat/0406207</a> <li>Takashi Nishikawa, Adilson E. Motter, Ying-Cheng Lai and Frank C. Hoppensteadt, "Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?" <a href="http://arxiv.org/abs/cond-mat/0306625">cond-mat/0306625</a> <li>E. Oh, K. Rho, H. Hong and B. Kahng, "Modular synchronization in complex networks", <a href="http://arxiv.org/abs/cond-mat/0408202">cond-mat/0408202</a> <li>Juan G. Restrepo, Edward Ott and Brian R. Hunt <ul> <li>"Spatial Patterns of Desynchronization Bursts in Networks", <a href="http://arxiv.org/abs/nlin.CD/0401007">nlin.CD/0401007</a> <li>"Emergence of Coherence in Complex Networks of Heterogeneous Dynamical Systems", <a href="http://dx.doi.org/10.1103/PhysRevLett.96.254103">Physical Review Letters</cite> <strong>96</strong> (2006): 254103</a> = <a href="http://arxiv.org/abs/cond-mat/0601639">cond-mat/0601639</a> </ul> <li>Marc Timme, "Revealing Network Connectivity From Dynamics", <a href="http://arxiv.org/abs/cond-mat/0610188">cond-mat/0610188</a> </ul>