Synchronization

Last update: 06 Feb 2026 14:16
First version: 3 July 2006 or earlier

Synchronization in the brain probably deserves its own notebook. So does the influence of network toplogy on synchronization.

Things to work on: how well does the "generalized synchrony" notion itself generalize to systems with stochastic dynamics?

Arkady Pikovsky, Michael Rosenblum and Jürgen Kurths, Synchronization: A Universal Concept in Nonlinear Sciences
Arthur Winfree, The Geometry of Biological Time

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
Roberto F. Galán, G. Bard Ermentrout, and Nathaniel N. Urban, "Efficient Estimation of Phase-Resetting Curves in Real Neurons and its Significance for Neural-Network Modeling", Physical Review Letters 94 (2005): 158101
Jürgen Jost and M. P. Joy, "Spectral Properties and Synchronization in Coupled Map Lattices," Physical Review E 65 (2002): 016201 = nlin.CD/0110037
Milan Palus [to whom thanks for reprints]
- and Vladimir Komarek, Zbynek Hrncir and Katalin Sterbova, "Synchronization as adjustment of information rates: Detection from bivariate time series", Physical Review E 63 (2001): 046211
- and Aneta Stefanovska, "Direction of coupling from phases of interacting oscillators: An information-theoretic approach", Physical Review E 67 (2003): 055201
Philippe Rigollet, "The Mean-Field Dynamics of Transformers", arxiv:2512.01868 [This is not a connection that would ever have occurred to me]
R. Quian Quiroga, A. Kraskov, T. Kreuz and P. Grassberger, "Performance of different synchronization measures in real data: A case study on electroencephalographic signals," Physical Review E 65 (2002): 041903 = nlin.CD/0109023 [See also the interesting "Comment" by R. B. Duckrow and A. M. Albano, PRE 67 (2003): 063901, and the reply by the original authors, 063902 in the same volume]

Kristina Lisa Klinkner, CRS, and Marcelo F. Camperi, "Measuring Shared Information and Coordinated Activity in Neuronal Networks", q-bio.NC/0506009

Juan A. Acebrón, L. L. Bonilla, Conrad J. Pérez Vicente, Félix Ritort and Renato Spigler, "The Kuramoto model: A simple paradigm for synchronization phenomena ", Reviews of Modern Physics 77 (2005): 137--186
R. E. Amritkar, Sarika Jalan and Chin-Kun Hu, "Synchronized clusters in coupled map networks. II. Stability analysis", Physical Review E 72 (2005): 016212
C. Anteneodo, A. M. Batista and R. L. viana, "Chaos synchronization in long-range coupled map lattices", nlin.CD/0401034
C. Anteneodo, S. E. de S. Pinto, A. M. Batista and R. L. Viana, "Analytical results for coupled map lattices with long-range interactions", nlin.CD/0308014
Fernando Antoneli, Ana Paula S Dias, Martin Golubitsky and Yunjiao Wang, "Patterns of synchrony in lattice dynamical systems", Nonlinearity 18 (2005): 2193--2209
Toru Aonishi and Masato Okada, "Dynamically-Coupled Oscillators: Cooperative Behavior via Dynamical Interaction," cond-mat/0207506
Alex Arenas, Albert Diaz-Guilera, Jurgen Kurths, Yamir Moreno, Changsong Zhou, "Synchronization in complex networks", Physics Reports 469 (2008): 93--153, arxiv:0805.2976
L. Arnhold, Peter Grassberger, K. Lehnertz and C. E. Elger, Physica D 134 (1999): 419
Fatihcan M. Atay
- "Distributed Delays Facilitate Amplitude Death of Coupled Oscillators", nlin.AO/0312050 = Physical Review Letters 91 (2003): 094101
- "Total and partial amplitude death in networks of diffusively coupled oscillators", nlin.AO/0401033 = Physica D 183 (2003): 1--18
Franco Bagnoli and Raul Rechtman, "Synchronization universality classes and stability of smooth, coupled map lattices", cond-mat/0507205
M. S. Baptista, T. Pereira, J. C. Sartorelli, I. L. Caldas and J. Kurths, "Phase Synchronization and invariant measures in sinusoidally perturbed chaotic systems", cond-mat/0507715
Stephan Bialonski and Klaus Lehnertz, "Identifying phase synchronization clusters in spatially extended dynamical systems", Physical Review E 74 (2006): 051909
Juan C. Botero and Jean-Jacques E. Slotine, "Examples of Synchronization in Discrete Chaotic Systems", nlin.CD/0609064
Michael A. Buice and Carson C. Chow, "Correlations, fluctuations and stability of a finite-size network of coupled oscillators", arxiv:0704.1650
A. Carpio, "Wave trains, self-oscillations and synchronization in discrete media", cond-mat/0506119
Mario Chavez, Claude Adam, Vincent Navarro, Stefano Boccaletti and Jacques Martinerie, "On the intrinsic time scales involved in synchronization: A data-driven approach", Chaos 15 (2005): 023904
Lauren M. Childs and Steven H. Strogatz, "Stability diagram for the forced Kuramoto model", arxiv:0807.4717
L. Cisneros, J. Jimenez, M. G. Cosenza, and A. Parravano, "Information transfer and nontrivial collective behavior in chaotic coupled map networks," nlin.CD/0202010
M. Escalona-Moran, M. G. Cosenza, P. Guillen and P. Coutin, "Synchronization and clustering in electroencephalographic signals", nlin.CD/0506014
Hirokazu Fujisaka and Masayoshi Inoue, "Statistical-physical theory of multivariate temporal fluctations: Global characterization and temporal correlation", Physical Review A 41 (1990): 5302--5319 [Finite-size scaling in the Kuramoto model, really]
Hirokazu Fujisaka, Satoki Uchiyama and Takehiko Horita, "Mapping Model of Chaotic Phase Synchronization", nlin.CD/0506010
P. Garcia, A. Parravano, M. G. Cosenza, J. Jimenez, and A. Marcano, "Coupled Map Networks as Communication Schemes," nlin.CD/0201042
Alexander E. Hramov and Alexey A. Koronovskii, "Generalized synchronization: a modified system approach", nlin.CD/0506023
Alexander E. Hramov, Alexey A. Koronovskii, Mariya K. Kurovskaya, and Olga I. Moskalenko, "Synchronization of spectral components and its regularities in chaotic dynamical systems", Physical Review E 71 (2005): 056204
Ali Jadbabaie, Nader Motee and Mauricio Barahona, "On the stability of the Kuramoto model of coupled nonlinear oscillators", math.OC/0504419
Sarika Jalan, R. E. Amritkar and Chin-Kun Hu, "Synchronized clusters in coupled map networks. I. Numerical studies", Physical Review E 72 (2005): 016211
Sarika Jalan, Fatihcan M. Atay and Jürgen Jost
- "Detection of synchronised chaos in coupled map networks using symbolic dynamics", nlin.CD/0510057
- "Symbolic synchronization and the detection of global properties of coupled dynamics from local information", Chaos 16 (2006): 033124 = nlin.CD/0604016
Jürgen Jost and Kiran M. Kolwankar, "Global Analysis of Synchronization in Coupled Maps", International Journal of Bifurcations and Chaos 16 (2006): 3695--3703
I. Kanter, W. Kinzel and E. Kanter, "Secure exchange of information by synchronization of neural networks," cond-mat/0202112
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence [Now re-issued as a cheap Dover paperback]
Susanna C. Manrubia, Alexander S. Mikhailov and Damian H. Zanette, Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems
Arturo C. Martí and C. Masoller, "Delay-induced Synchronization Phenomena in an Array of Globally Coupled Logistic Maps," nlin.CD/0212037
Norbert Marwan, M. Thiel, N. R. Nowaczyk, "Cross Recurrence Plot Based Synchronization of Time Series," physics/0201062
M. S. O. Massunaga and M. Bahiana, "Synchronization in large populations of limit cycle oscillators with long-range interactions," cond-mat/0201508
Patrick McGraw and Michael Menzinger, "Analysis of Nonlinear Synchronization Dynamics of Oscillator Networks by Laplacian Spectral Methods", cond-mat/0610522
P. K. Mohanty and Antonio Politi, "Partial synchronization of globally coupled oscillators", cond-mat/0507037
Roberto Monetti, Wolfram Bunk, Thomas Aschenbrenner and Ferdinand Jamitzky, "Characterizing synchronization in time series using information measures extracted from symbolic representations", Physical Review E 79 (2009): 046207
Ernest Montbrió, Jürgen Kurths and Bernd Blasius, "Synchronization of two interacting populations of oscillators", nlin.AO/0406004
Markus Muller, Gerold Baier, Andreas Galker, Ulrich Stephani and Hiltrud Muhle, "Detection and characterization of changes of the correlation structure in multivariate time series", PRE 71 (2005): 046116
Miguel A. Munoz and Romualdo Pastor-Satorras, "Stochastic theory of synchronization transitions in extended systems," cond-mat/0301059
Amitabha Nandi, G. Santhosh, R. K. Brojen Singh, Ram Ramaswamy, "The synchronization of stochastic oscillators", q-bio.QM/0608022
Grigory V. Osipov, Mikhail V. Ivanchenko, Jurgen Kurths, and Bambi Hu, "Synchronized chaotic intermittent and spiking behavior in coupled map chains", Physical Review E 71 92005): 056209
Per Ostborn, S. Aberg and G. Ohlen, "Phase transitions towards frequency entrainment in large oscillator lattices," cond-mat/0302234
Edward Ott, John H. Platig, Thomas M. Antonsen, Michelle Girvan, "Echo Phenomena in Large Systems of Coupled Oscillators", arxiv:0807.4499 [Sounds cool]
Diego Pazo, "Thermodynamic limit of the first-order phase transition in the Kuramoto model", nlin.AO/0509020
M. Pineda and M. G. Cosenza, "Synchronization in driven versus autonomous coupled chaotic maps", Physical Review E 71 (2005): 057201
R. Quian Quiroga, L. Arnhold and Peter Grassberger, Physical Review E 61 (2000): 5142
R. Quian Quiroga, T. Kreuz and Peter Grassberger, "Event synchronization: a simple and fast method to measure synchronicity and time delay patterns," nlin.CD/0202065
Govindan Rangarajan and Mingzhou Ding, "Stability of Synchronized Chaos in Coupled Dynamical Systems," nlin.CD/0201037
David C. Roberts, "Linear Reformulation of the Kuramoto Model of Self-Synchronizing Coupled Oscillators", Physical Review E 77 (2008): 031114
Nikolai F. Rulkov and Valentin S. Afraimovich, "Detectability of non-differentiable generalized synchrony," nlin.CD/0303022
Nikolai F. Rulkov, M. S. Sushcik, Lev S. Tsimring and Henry D. I. Abarbanel, Physical Review E 51 (1995): 980
Philip Seliger, Stephen C. Young, and Lev S. Tsimring, "Plasticity and learning in a network of coupled phase oscillators," nlin.AO/0110044
A. Shabunin, V. Astakhov and Jurgen Kurths, "Quantitative analysis of chaotic synchronization by means of coherence", Physical Review E 72 (2005): 016218
E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, "Inverse Anticipating Synchronization," nlin.CD/0111011
Michael Small and Kevin Judd, "Detecting periodicity in experimental data using linear modeling techniques", physics/9810021 [Not strictly synchrony measurement, but closely related]
Hiromichi Suetani, Yukito Iba and Kazuyuki Aihara
- "Detecting Generalized Synchronization Between Chaotic Signals: A Kernel-based Approach", Journal of Physics A: Mathematical and General 39 (2006) 10723--10742, nlin.CD/0507006
- "Detecting Generalized Synchronization of Chaotic Dynamical Systems: A Kernel-based Method and Choice of Its Parameter", nlin.CD/0507041
Jun-nosuke Teramae and Yoshiki Kuramoto, "Strong Desynchronizing Effects of Weak Noise in Globally Coupled Systems," nlin.CD/0102006
Xiao Fan Wang, "Slower Speed and Stronger Coupling: Adaptive Mechanisms of Self-Organized Chaos Synchronization," cond-mat/0109395
Damian H. Zanette
- "Disturbing synchronization: Propagation of perturbations in networks for coupled oscillators", cond-mat/0412356
- "Propagating structures in globally coupled systems with time delays," Physical Review E 62 (2000): 3167--3172
- "Propagation of small perturbations in synchronized oscillator networks", cond-mat/0409159
- "Synchronization and frustration in oscillator networks with attractive and repulsive interactions", cond-mat/0509063
Damian H. Zanette and Alexander S. Mikhailov, "Dynamical systems with time-dependent coupling: clustering and critical behavior", Physica D 194 (2004): 203--218