Synchronization by reactive coupling and nonlinear frequency pulling

M. C. Cross, J. L. Rogers, Ron Lifshitz, and A. Zumdieck
Phys. Rev. E 73, 036205 – Published 6 March 2006

Abstract

We present a detailed analysis of a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling. We study the model for the mean field case of all-to-all coupling, deriving results for the initial onset of synchronization as the coupling or nonlinearity increase, and conditions for the existence of the completely synchronized state when all the oscillators evolve with the same frequency. Explicit results are derived for the Lorentzian, triangular, and top-hat distributions of oscillator frequencies. Numerical simulations are used to construct complete phase diagrams for these distributions.

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  • Received 3 October 2005

DOI:https://doi.org/10.1103/PhysRevE.73.036205

©2006 American Physical Society

Authors & Affiliations

M. C. Cross

  • Department of Physics 114-36, California Institute of Technology, Pasadena, California 91125, USA

J. L. Rogers

  • HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, California 90265, USA

Ron Lifshitz

  • School of Physics & Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel

A. Zumdieck

  • Max Planck Institute for Physics of Complex Systems, Noethnitzer Strasse 38, 01187 Dresden, Germany

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Vol. 73, Iss. 3 — March 2006

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