The Kuramoto model: A simple paradigm for synchronization phenomena

By J. Acebrón, Luis L. Bonilla, C. P. Vicente, Felix Ritort, R. Spigler. 2005

2,926 citations recorded by the source corpus.

Subfields: Cognitive Neuroscience, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6ce6aa385045b19268f0620c9192028df51f65e6

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Citations in the corpus

Coupling functions:universal insights into dynamical interaction mechanisms (2017, methodology): “…intricate, manifesting a whole range of qualitatively different states, physical effects, phenomena and characteristics, including synchronization (Acebrón et al., 2005; Kapitaniak et al., 2012; Lehnertz and Elger, 1998; Pikovsky et al., 2001), oscillation and amplitude death (Koseska et al.,…”
Spatial beam self-cleaning in multimode fibres (2016, background): “ding spatiotemporal solitons [6, 7, 8], spatiotemporal rogue waves and turbulence [29], and extend the synchronization of coupled nonlinear oscillators, as described for example by the Kuramoto model [30], to spatially extended natural systems. Moreover, presented results may stimulate new theoretic”
The dynamics of chimera states in heterogeneous Kuramoto networks (2009, background): “One of the simplest such networks is the Kuramoto model, where each oscillator is described by a single angular variable (or phase), and the oscillators interact via a trigonometric function of phase differences [4–6].”
Long-Time Behaviour and Phase Transitions for the Mckean–Vlasov Equation on the Torus (2018, background): “Finally, let us mention that there is a larger picture in the Kuramoto model when different frequency oscillators are allowed, see [1] for a nice review of the subject and [19] for recent numerical work on phase transitions for this problem.”
Low-dimensional dynamics of populations of pulse-coupled oscillators (2013, methodology): “The Kuramoto model has motivated a great deal of theoretical work and has been investigated under countless variations and used to model a number of physical, chemical, biological, social, and technological systems [3,11–13].”
Critical phenomena in complex networks (2007, methodology): “The value of the upper critical dimension of the Kuramoto model is still under discussion (Acebrón et al., 2005).”
Emerging concepts for the dynamical organization of resting-state activity in the brain (2010, positive): “In general, networks of oscillators show — in the absence of delays — trivial global dynamics, namely full synchronization 57,58 , whereas more complex dynamics emerge if delays and noise are introduced, as in the models by Ghosh et al. 37 and Deco et al. 38 .”
The Kuramoto model in complex networks (2015, methodology): “Despite the progress achieved in the last years in understanding the effects of inertia [4], the theory discussed still has some fundamental limitations.”
On a Bio-inspired Amphibious Robot Capable of Multimodal Motion (2012, neutral): “movements of multiple joints [22], [24] ⎧⎨ ⎩ φ̇i = 2πfi + ∑ j∈T (i) ajwij sin(φj − φi − γij ) äi = τi { τi 4 (Ai − ai) − ȧi }”
Nonlinear Auto-Oscillator Theory of Microwave Generation by Spin-Polarized Current (2009, background): “In general, the nonzero coupling phases could introduce frustration into the system of oscillators [135].”
Phase reduction approach to synchronisation of nonlinear oscillators (2016, methodology): “See [2, 24, 25] for the detailed analysis of the Kuramoto and related models.”
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization (2016, methodology): “In the absence of inertia, T = 0 reproduces the Kuramoto model [23, 237, 238], while T 6= 0 gives the model of Ref.”