## From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators (2000)

Venue: | Phys. D |

Citations: | 141 - 3 self |

### BibTeX

@ARTICLE{Strogatz00fromkuramoto,

author = {Steven H. Strogatz},

title = {From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators},

journal = {Phys. D},

year = {2000},

pages = {1--20}

}

### Years of Citing Articles

### OpenURL

### Abstract

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.

### Citations

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(Show Context)
Citation Context ...ics and engineering, from arrays of lasers [22,23] and microwave oscillators [24] to superconducting Josephson junctions [25,26]. Collective synchronization was first studied mathematically by Wiener =-=[27,28]-=-, who recognized its ubiquity in the natural world, and who speculated that it was involved in the generation of alpha rhythms in the brain. Unfortunately Wiener’s mathematical approach based on Fouri... |

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Citation Context ...ics and engineering, from arrays of lasers [22,23] and microwave oscillators [24] to superconducting Josephson junctions [25,26]. Collective synchronization was first studied mathematically by Wiener =-=[27,28]-=-, who recognized its ubiquity in the natural world, and who speculated that it was involved in the generation of alpha rhythms in the brain. Unfortunately Wiener’s mathematical approach based on Fouri... |

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(Show Context)
Citation Context ...ve recently been measured for the first time [16]); metabolic synchrony in yeast cell suspensions [17,18]; congregations of synchronously flashing fireflies [19,20]; and crickets that chirp in unison =-=[21]-=-. There are also many examples in physics and engineering, from arrays of lasers [22,23] and microwave oscillators [24] to superconducting Josephson junctions [25,26]. Collective synchronization was f... |

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(Show Context)
Citation Context ...emaker cells in the suprachiasmatic nucleus of the brain (where the individual cellular frequencies have recently been measured for the first time [16]); metabolic synchrony in yeast cell suspensions =-=[17,18]-=-; congregations of synchronously flashing fireflies [19,20]; and crickets that chirp in unison [21]. There are also many examples in physics and engineering, from arrays of lasers [22,23] and microwav... |

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Citation Context ...here the individual cellular frequencies have recently been measured for the first time [16]); metabolic synchrony in yeast cell suspensions [17,18]; congregations of synchronously flashing fireflies =-=[19,20]-=-; and crickets that chirp in unison [21]. There are also many examples in physics and engineering, from arrays of lasers [22,23] and microwave oscillators [24] to superconducting Josephson junctions [... |

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Citation Context ...f collisionless plasmas [38–48]. Not only that, he explained, but similar phenomena occur in many other parts of science, in connection with instabilities of ideal shear flows [49–51], solitary waves =-=[52,53]-=-, bubbly fluids [54], and resonance poles in atomic systems [55]. Wow—Iwastalking to the right guy. He went on to explain some of his own work. He was trying to write amplitude equations for a weakly ... |

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(Show Context)
Citation Context ...f collisionless plasmas [38–48]. Not only that, he explained, but similar phenomena occur in many other parts of science, in connection with instabilities of ideal shear flows [49–51], solitary waves =-=[52,53]-=-, bubbly fluids [54], and resonance poles in atomic systems [55]. Wow—Iwastalking to the right guy. He went on to explain some of his own work. He was trying to write amplitude equations for a weakly ... |