Numerical Bifurcation Analysis on a System of Coupled Crystal Oscillators

  • Steven ReevesEmail author
  • Antonio Palacios
  • Patrick Longhini
  • Visarath In
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 6)


A coupled crystal oscillator system has been proposed as an alternative to GPS for precision timing applications. The system of differential equations governing the dynamics is inherently nonlinear and has 4N degrees of freedom. Even though the system is highly complex, we can provide analytic restrictions on the types of solutions by observing the dynamic symmetry of the device. In this paper we examine numerically generated bifurcation diagrams, for specific values of N, in order to illustrate which solutions predicted by the symmetry analysis exist and are stable. The results from this study allows us to better understand how the device will behave when it is constructed.


Hopf Bifurcation Coupling Strength Bifurcation Diagram Isotropy Subgroup Hopf Bifurcation Point 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Steven Reeves
    • 1
    Email author
  • Antonio Palacios
    • 2
  • Patrick Longhini
    • 3
  • Visarath In
    • 3
  1. 1.University of CaliforniaSanta CruzUSA
  2. 2.San Diego State UniversitySan DiegoUSA
  3. 3.SPAWAR Systems Center PacificSan DiegoUSA

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