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Transition to phase synchronization in coupled periodically driven chaotic pendulums.

H L Yang1

  • 1Department of Physics, University of Potsdam, Am Neuen Palais, Postfach 601553, D-14415 Potsdam, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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We studied phase synchronization transitions in coupled pendulums. For identical pendulums, synchronization loss occurs at a blowout bifurcation, coinciding with hyperchaos-chaos transitions, showing intermittency. Non-identical pendulums exhibit different transition dynamics.

Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Chaos theory

Background:

  • Phase synchronization is crucial in coupled nonlinear systems.
  • Understanding transitions between synchronized and desynchronized states is key.
  • Periodically driven pendulums serve as a model for complex dynamics.

Purpose of the Study:

  • To investigate the transition to phase synchronization in coupled periodically driven pendulums.
  • To analyze the role of bifurcations and chaos transitions in synchronization.
  • To compare dynamics for identical versus non-identical pendulum systems.

Main Methods:

  • Analysis of invariant subspaces in coupled systems.
  • Identification of blowout bifurcations.
  • Characterization of on-off intermittency and basin structures.

Related Experiment Videos

  • Comparison of dynamics for identical and non-identical units.

    • Main Results:

    • For identical pendulums, synchronization-desynchronization transitions occur at blowout bifurcations, coinciding with hyperchaos-chaos transitions.
    • On-off intermittency and intermingled basins of attraction are observed near this transition for identical pendulums.
    • For non-identical pendulums, the synchronization-desynchronization transition occurs beyond the hyperchaos-chaos transition, with distinct basin structures and intermittency statistics.

    Conclusions:

    • The nature of phase synchronization transitions depends significantly on whether the coupled units are identical or non-identical.
    • Blowout bifurcations play a critical role in synchronization transitions for identical driven pendulums.
    • System asymmetry in non-identical pendulums leads to different routes to desynchronization and associated chaotic phenomena.