Synchronization: A Universal Concept in Nonlinear Sciences

By A. Pikovsky, M. Rosenblum, Jürgen Kurths. 2001

7,314 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9736697983b377b7d445d5af1c7d8c8bfd4ecd2c

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Citations in the corpus

Oscillation quenching mechanisms: Amplitude vs. oscillation death (2013, background): “To start with, weak coupling of nonlinear oscillators leads to synchronization, a fundamental nonlinear phenomenon in various fields of science [17–19].”
Synchronization and desynchronization in epilepsy: controversies and hypotheses (2012, background): “As there are several valid methods of computation, and measurements can be taken on different types of signals and across different spatial scales, the results should be always interpreted with appropriate attention to context (Varela et al. 2001; Pikovsky et al. 2003).”
Self-oscillation (2011, background): “Though the quantitative characterization of entrainment can be cumbersome (see [105, 124, 126, 144]), the qualitative explanation of the kind of entrainment shown in Fig.”
Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics (2005, background): “Sudden changes in phase were designated phase slip [78].”
Evaluation of different measures of functional connectivity using a neural mass model (2004, background): “Phase synchronisation between two oscillators is a ubiquitous phenomenon, which appears when they are coupled in a broad range of structures, including MEG or EEG generators (Pikovsky et al., 2001).”
The concept of entrainment and its significance for ethnomusicology (2004, methodology): “It also demonstrates that in music we are rarely, if at all, dealing with strictly periodic oscillations, but exact periodicity has been shown to be not a prerequisite for entrainment (e.g. Pikovsky et al. 2001).”
Partial synchronization: from symmetry towards stability (2002, background): “A large number of examples of synchronization in nature can be found in [8], and references therein.”
A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model (2010, background): “On the other hand, if K is sufficiently large, it is numerically observed that some of oscillators or all of them tend to rotate at the same velocity on average, which is called the synchronization [38, 43].”
Adaptive synchronization of uncertain dynamical networks with delayed coupling (2008, background): “In biology, synchronization of coupled systems is a commonly used model, and the presence, absence, or degree of synchronization can be an important part of the function or dysfunction of a biological system [ 16 ].”
On partial contraction analysis for coupled nonlinear oscillators (2004, background): “The threshold phenomenon described by inequality (17) is also reminiscent of phase transitions in physics [55] and of Bose-Einstein condensation [28] .”
Community detection in graphs (2009, background): “Synchronization (Pikovsky et al., 2001) is an emergent phenomenon occurring in systems of interacting units and is ubiquitous in nature, society and technology.”
Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay (2006, background): “5] and τ ∈ [9, 10] as indicated in the Fig.”
The dynamics of resting fluctuations in the brain: metastability and its dynamical cortical core (2016, unknown): “If the linear coupling (following a Taylor expansion of the full coupling) does not exist, the next non-vanishing higher order term should be considered, which is a case we do not address here (please see Kuramoto 59 (see Eq 5.3.1) and Pikovsky, Arkady and Kurths 60 (see Eq.”
Oscillators that sync and swarm (2017, methodology): “(3) and (4) with A= B= 1 and vi=ωi= 0 in the (J, K) plane.”
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization (2016, background): “Since then, synchronization has captivated the interest of scientists and, nowadays, it is investigated in fields as diverse as natural and social sciences [8], or engineering [4].”