## Synchronization

*27 Feb 2017 16:30*

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]
- 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

- and Vladimir
Komarek, Zbynek Hrncir and Katalin Sterbova, "Synchronization as adjustment of
information rates: Detection from bivariate time series", Physical Review
E
- 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

- "Distributed Delays Facilitate Amplitude Death of Coupled
Oscillators", nlin.AO/0312050
= Physical Review Letters
- 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", 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

- "Detecting Generalized Synchronization Between Chaotic
Signals: A Kernel-based
Approach", nlin.CD/0507006
= Journal of Physics A: Mathematical and
General
- 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