## On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators (2004)

Venue: | In Proceedings of the American Control Conference |

Citations: | 58 - 8 self |

### BibTeX

@INPROCEEDINGS{Jadbabaie04onthe,

author = {Ali Jadbabaie and Nader Motee and Mauricio Barahona},

title = {On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators},

booktitle = {In Proceedings of the American Control Conference},

year = {2004},

pages = {4296--4301}

}

### Years of Citing Articles

### OpenURL

### Abstract

We provide a complete analysis of the Kuramoto model of coupled nonlinear oscillators with uncertain natural frequencies and arbitrary interconnection topology. Our work extends and supersedes existing, partial results for the case of an all-to-all connected network. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase di#erences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.