Chapman-Enskog method and synchronization of globally coupled oscillators

Details Chapman-Enskog method and synchronization of globally coupled oscillators Chapman-Enskog method and synchronization of globally coupled oscillators

2000-06-12

arxiv.org/abs/cond-mat/0006195v2

Phys. Rev. E 62, 4862-4868 (2000)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 2-column Revtex, no figures, minor changes

Scientific paper

10.1103/PhysRevE.62.4862

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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