From Kardar-Parisi-Zhang scaling to explosive desynchronization in arrays of limit-cycle oscillators

Roland Lauter, Aditi Mitra, and Florian Marquardt
Phys. Rev. E 96, 012220 – Published 24 July 2017

Abstract

Phase oscillator lattices subject to noise are one of the most fundamental systems in nonequilibrium physics. We have discovered a dynamical transition which has a significant impact on the synchronization dynamics in such lattices, as it leads to an explosive increase of the phase diffusion rate by orders of magnitude. Our analysis is based on the widely applicable Kuramoto-Sakaguchi model, with local couplings between oscillators. For one-dimensional lattices, we observe the universal evolution of the phase spread that is suggested by a connection to the theory of surface growth, as described by the Kardar-Parisi-Zhang (KPZ) model. Moreover, we are able to explain the dynamical transition both in one and two dimensions by connecting it to an apparent finite-time singularity in a related KPZ lattice model. Our findings have direct consequences for the frequency stability of coupled oscillator lattices.

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  • Received 3 August 2016
  • Revised 7 May 2017

DOI:https://doi.org/10.1103/PhysRevE.96.012220

©2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

Roland Lauter1,2, Aditi Mitra3, and Florian Marquardt1,2

  • 1Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
  • 2Max Planck Institute for the Science of Light, Staudtstr. 2, 91058 Erlangen, Germany
  • 3Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA

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Issue

Vol. 96, Iss. 1 — July 2017

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