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Chapman-Enskog method and synchronization of globally coupled oscillators

L. L. Bonilla
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Abstract

The Chapman-Enskog method of kinetic theory is applied to two problems of synchronization of globally coupled phase oscillators. First, a modified Kuramoto model is obtained in the limit of small inertia from a more general model which includes ``inertial'' effects. Second, a modified Chapman-Enskog method is used to derive the amplitude equation for an O(2) Takens-Bogdanov bifurcation corresponding to the tricritical point of the Kuramoto model with a bimodal distribution of oscillator natural frequencies. This latter calculation shows that the Chapman-Enskog method is a convenient alternative to normal form calculations.

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L. L. Bonilla. 2000-07-10. Chapman-Enskog method and synchronization of globally coupled oscillators. https://doi.org/10.1103/physreve.62.4862

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