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On the Problem of Synchronization of Identical Dynamical Systems: The Huygens’s Clocks

In: Variational Analysis and Aerospace Engineering

Author

Listed:
  • Rui Dilão

    (Instituto Superior Técnico Av. Rovisco Pais)

Abstract

In 1665, Christiaan Huygens reported the observation of the synchronization of two pendulum clocks hanged on the wall of his workshop. After synchronization, the clocks swung exactly in the same frequency and 180° out of phase—anti-phase synchronization. Here, we propose and analyze a new interaction mechanism between oscillators leading to exact anti-phase and in-phase synchronization of pendulum clocks, and we determine a sufficient condition for the existence of an exact anti-phase synchronous state. We show that exact anti-phase and in-phase synchronous states can coexist in phase space, and the periods of the synchronous states are different from the eigenperiods of the individual oscillators. We analyze the robustness of the system when the parameters of the individual pendulum clocks are varied, and we show numerically that exact anti-phase and in-phase synchronous states exist in systems of coupled oscillators with different parameters.

Suggested Citation

  • Rui Dilão, 2009. "On the Problem of Synchronization of Identical Dynamical Systems: The Huygens’s Clocks," Springer Optimization and Its Applications, in: Variational Analysis and Aerospace Engineering, chapter 0, pages 163-181, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-95857-6_10
    DOI: 10.1007/978-0-387-95857-6_10
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