Synchronization
Last update: 21 Apr 2025 21:17
First version:
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?
See also:
Complex Networks;
Dynamics;
Excitable Media;
Neural Coding;
Synchronization in Neural Systems
Recommended, big picture:
- Arkady Pikovsky, Michael Rosenblum and Jürgen Kurths,
Synchronization: A Universal Concept in Nonlinear Sciences
- Arthur Winfree, The Geometry of Biological Time
Recommended, close-ups:
- 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]
- 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]
Modesty forbids me to recommend:
- Kristina Lisa Klinkner, CRS, and Marcelo F. Camperi, "Measuring
Shared Information and Coordinated Activity in Neuronal Networks", q-bio.NC/0506009
To read:
- 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
- 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", nlin.CD/0507006
= Journal of Physics A: Mathematical and
General 39 (2006) 10723--10742
- "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