Coupled Crystal Oscillator System and Timing Device

  • Antonio PalaciosEmail author
  • Pietro-Luciano Buono
  • Visarath In
  • Patrick Longhini
Conference paper
Part of the Understanding Complex Systems book series (UCS)


At the National Observatory in Washington D.C., time is measured by averaging the times of an uncoupled ensemble. The measurements show a scaling law for phase-error reduction as, where is the number of crystals in the ensemble. Analytical and computational works show that certain patterns of collective behavior produced by a network of nonlinear oscillators leads to optimal phase-error that scales down as. In this talk we use symmetry-based methods to classify all possible patterns of oscillations, and their stability properties. Then we show why, among all possible patterns, a traveling wave, in which consecutive oscillators are out of phase by, yields the best phase-error reduction. Finally, we prove, analytically, that is the fundamental limit of of phase-error reduction that can be obtained with a network of nonlinear oscillators of any type, not just crystals.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Antonio Palacios
    • 1
    Email author
  • Pietro-Luciano Buono
    • 2
  • Visarath In
    • 3
  • Patrick Longhini
    • 3
  1. 1.Nonlinear Dynamical Systems Group, Department of MathematicsSan Diego State UniversitySan DiegoUSA
  2. 2.Faculty of ScienceUniversity of Ontario Institute of TechnologyOshawaCanada
  3. 3.Space and Naval Warfare Systems CenterSan DiegoUSA

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