Network of Coupled Oscillators for Precision Timing

  • Pietro-Luciano BuonoEmail author
  • Bernard Chan
  • Jocirei Ferreira
  • Patrick Longhini
  • Antonio Palacios
  • Steven Reeves
  • Visarath In
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 6)


Precise time dissemination and synchronization have been some of the most important technological tasks for several centuries. It was realized that precise time-keeping devices having the same stable frequency and precisely synchronized can have important applications in navigation. Satellite-based global positioning and navigation systems such as the GPS use the same principle. However, even the most sophisticated satellite navigation equipment cannot operate in every environment. In response to this need, we present a computational and analytical study of a network based model of a high-precision, inexpensive, Coupled Oscillator System and Timing device. Preliminary results from computer simulations seem to indicate that timing errors decrease as 1 / N when N crystals are coupled as oppose to \(1{/}\sqrt{N}\) for an uncoupled assemble. This manuscript is aimed, however, at providing a complete classification of the various patterns of collective behavior that are created, mainly, through symmetry-breaking bifurcations. The results should provide guidelines for follow-up simulations, design and fabrication tasks.


Periodic Solution Irreducible Representation Hopf Bifurcation Hopf Bifurcation Point Crystal Oscillator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Visarath In, Antonio Palacios, and Pietro-Luciano Buono are conducting (as part of on-going work) all the theoretical calculations on the generic nonlinear system, as well as on specific applications. Antonio Palacios was supported by ASEE ONR Summer Faculty.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Pietro-Luciano Buono
    • 1
    Email author
  • Bernard Chan
    • 2
  • Jocirei Ferreira
    • 3
  • Patrick Longhini
    • 4
  • Antonio Palacios
    • 2
  • Steven Reeves
    • 2
  • Visarath In
    • 4
  1. 1.Faculty of ScienceUniversity of Ontario Institute of TechnologyOshawaCanada
  2. 2.Nonlinear Dynamical Systems Group, Department of MathematicsSan Diego State UniversitySan DiegoUSA
  3. 3.Institute of Exact and Earth Science-CUA, Federal University of Mato GrossoCuiabáBrazil
  4. 4.Space and Naval Warfare Systems Center, Code 2363San DiegoUSA

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