Time Delay in the Kuramoto Model of Coupled Oscillators

1998/07/22 by M. K. Stephen Yeung, Steven H. Strogatz · 6 citations
Physics and Astronomy · #chao-dyn #nlin.CD

paper · pdf · doi:10.1103/physrevlett.82.648

published as Phys. Rev. Lett., 82(3):648--651 (1999) · 4 pages, 1 revtex file + 4 eps files. Submitted to Phys. Rev. Lett. Also available at http://publish.aps.org/eprint/gateway/eplist/aps1998jul13_007

arxiv created 1998/07/22 · arxiv updated 2009/11/30

Abstract

We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive exact formulas for the stability boundaries of the incoherent and synchronized states, as a function of the delay, in the special case where the oscillators are identical. The experimental implications of the model are discussed for populations of chirping crickets, where the finite speed of sound causes communication delays, and for physical systems such as coupled phase-locked loops or lasers.

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