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Controlling chaos with simple limiters

Corron1, Pethel, Hopper

  • 1Dynetics, Inc., P.O. Box 5500, Huntsville, Alabama 35814, USA.

Physical Review Letters
|October 6, 2000
PubMed
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Simple controllers can effectively manage chaotic dynamics in physical systems like pendulums and circuits. This breakthrough in chaos control opens doors for wider practical applications in complex problems.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Control Theory

Background:

  • Chaotic systems, while complex, exhibit underlying unstable periodic orbits.
  • Controlling chaos often requires sophisticated methods relative to the system's complexity.

Purpose of the Study:

  • To demonstrate that simple controllers can effectively achieve chaos control.
  • To explore the application of minimal perturbations for controlling chaotic dynamics.

Main Methods:

  • Utilizing an adjustable, passive limiter as a controller.
  • Implementing a weight for a driven pendulum and a diode for a double scroll circuit.
  • Experimentally controlling multiple unstable periodic orbits.

Main Results:

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  • Successfully controlled chaotic dynamics in both a driven pendulum and a double scroll circuit.
  • Demonstrated the efficacy of simple, passive limiters as controllers.
  • Achieved selective control of multiple unstable periodic orbits with minimal perturbations.

    • Conclusions:

    • Chaos control is achievable with controllers significantly simpler than the controlled system.
    • The findings suggest broader practical applications for chaos control in diverse scientific and engineering fields.