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Related Experiment Videos

External feedback control of chaos using approximate periodic orbits.

Kazuyuki Yagasaki1, Moriyoshi Kumagai

  • 1Department of Mechanical and Systems Engineering, Gifu University, Gifu, Gifu 501-1193, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
Summary

External feedback controls chaos in physical systems by targeting unstable periodic orbits. This method was validated in simulations and experiments with pendulum systems.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Control Theory

Background:

  • Chaos theory describes complex, unpredictable behavior in deterministic systems.
  • Controlling chaos is crucial for understanding and manipulating nonlinear phenomena.
  • External feedback is a promising technique for stabilizing unstable states.

Purpose of the Study:

  • To apply the external feedback technique for controlling chaos in physical systems.
  • To extract unstable periodic orbits from chaotic time series using delay coordinate embedding.
  • To demonstrate the efficacy of the method in various dynamical systems.

Main Methods:

  • Utilized the external feedback technique.
  • Employed the delay coordinate technique to identify unstable periodic orbits from chaotic time series.

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  • Conducted numerical simulations and physical experiments.

    • Main Results:

    • Successfully controlled chaos in periodically forced, single- and two-degree-of-freedom systems.
    • Demonstrated the effectiveness of the external feedback technique in both simulations and experiments.
    • Validated the identification of unstable periodic orbits using delay coordinates.

    Conclusions:

    • The external feedback technique is an efficient method for controlling chaos in real physical systems.
    • The delay coordinate technique is effective for identifying target unstable periodic orbits.
    • The findings have implications for controlling complex dynamics in various scientific and engineering fields.