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The mathematics of asymptotic stability in the Kuramoto model.

ABSTRACT: Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the corresponding rigorous validation has long remained problematic and was achieved only recently. This paper reviews the mathematical results on asymptotic stability of stationary solutions in the continuum limit of the Kuramoto model, and provides insights into the principal arguments of proofs. This review is complemented with additional original results, various examples, and possible extensions to some variations of the model in the literature.

SUBMITTER: Dietert H

PROVIDER: S-EPMC6304033 | biostudies-literature | 2018 Dec

REPOSITORIES: biostudies-literature

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The mathematics of asymptotic stability in the Kuramoto model.

Dietert Helge H Fernandez Bastien B

Proceedings. Mathematical, physical, and engineering sciences 20181212 2220

Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the corresponding rigorous validation has long remained problematic and was achieved only recently. This paper reviews the mathematical results on asymptotic stability of stationary solutions in the continuum limit of the Kuramoto model, and provides insights into the princip ...[more]

PMID: 30602931

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