Title

Time Delay in the Kuramoto Model of Coupled Oscillators

Authors

Stephen M.K. Yeung, University of San FranciscoFollow
S H. Strogatz

Document Type

Article

Publication Date

1999

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.

Comments

Copyright 1999 American Physical Society

Article available at: http://dx.doi.org/10.1103/PhysRevLett.82.648

DOI

10.1103/PhysRevLett.82.648

Recommended Citation

M. K. Stephen Yeung and Steven H. Strogatz. Time Delay in the Kuramoto Model of Coupled Oscillators. Phys. Rev. Lett. 82, 648 (1999). Copyright American Physical Society.