From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

By Steven H. Strogatz. 2000

2,908 citations recorded by the source corpus.

The Kuramoto model describes a large population of coupled limit-cycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certain threshold, the system exhibits a phase transition: some of the oscillators spontaneously synchronize, while others remain incoherent. The mathematical analysis of this bifurcation has proved both problematic and fascinating. We review 25 years of research on the Kuramoto model, highlighting the false turns as well as the successes, but mainly following the trail leading from Kuramoto’s work to Crawford’s recent contributions. It is a lovely winding road, with excursions through mathematical biology, statistical physics, kinetic theory, bifurcation theory, and plasma physics. © 2000 Elsevier Science B.V. All rights reserved.

Subfields: Biomedical Engineering, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/52e9f7e03e5d8234bcf61ade5aea0e1db5f12536

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In Computer Networks and Communications

Citations in the corpus

What are higher-order networks? (2021, background): “For sufficiently strong coupling, the oscillators start to synchronize [163,255].”
Swarm dynamics and equilibria for a nonlocal aggregation model (2011, background): “As derived for example in [3], [4] (see also [30], [31] and references therein), this noise can be modelled by adding a diffusion term so that the continuous model (1a) becomes ρt +∇ · (ρv) = D∆ρ, (93) where D represents the noise strength.”
Coupling functions:universal insights into dynamical interaction mechanisms (2017, methodology): “Today this model is the cornerstone for many studies and applications (Acebrón et al., 2005; Strogatz, 2000), including neuroscience (Breakspear et al., 2010; Cabral et al., 2014; Cumin and Unsworth, 2007), Josephsonjunction arrays (Filatrella et al., 2000; Wiesenfeld et al., 1996, 1998), power…”
A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model (2010, background): “See [27] and [43] for Kuramoto’s discussion.”
Synchronization and power sharing for droop-controlled inverters in islanded microgrids (2012, neutral): “We refer to the recent surveys [1,28,12] for applications and theoretic results.”
Phase reduction approach to synchronisation of nonlinear oscillators (2016, methodology): “In particular, when the phase coupling function is given by the lowest order Fourier term as Γ(φ) = − sinφ, the model becomes the well-known Kuramoto model [2, 24, 25], given by”
On robust control algorithms for nonlinear network consensus protocols (2008, background): “1, consider the Kuramoto model [13] given by”
Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization (2010, methodology): “The properties of the so-called Kuramoto model [33]”
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.”
Algebraic Connectivity of Interdependent Networks (2014, background): “To date, the problem of how the structural properties of a network influences the convergence and stability of its synchronized states has been extensively investigated and discussed, both numerically and theoretically [5, 6, 7, 8, 9], with special attention given to networks of coupled oscillators ”
Synchronization from Second Order Network Connectivity Statistics (2011, background): “The order parameter is the length of the population vector (Strogatz, 2000) r N e i j j θ where i = − 1 and |·| represents the absolute value of the complex vector.”
Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators (2014, background): “Kd, 05.65.+b Mathematics Subject Classification: 34C15, 34C23, 35B36, 82C22, 82C44 (Some figures may appear in colour only in the online journal)”