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Chaos suppression in the parametrically driven Lorenz system.

Chol-Ung Choe1, Klaus Höhne, Hartmut Benner

  • 1Institut für Festkörperphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
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Chaos suppression in the Lorenz system was achieved using high-frequency parametric forcing. Theoretical criteria for this effect were derived and experimentally verified using numerical simulations and an analog electronic circuit.

Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Complex systems

Background:

  • The Lorenz system is a fundamental model for atmospheric convection and chaotic behavior.
  • Controlling chaotic systems is crucial for understanding and predicting complex phenomena.

Purpose of the Study:

  • To theoretically predict and experimentally verify chaos suppression in the Lorenz system.
  • To derive criteria for chaos suppression using parametric forcing.

Main Methods:

  • Theoretical prediction of chaos suppression criteria.
  • Numerical simulations of the Lorenz system with parametric forcing.
  • Experimental verification using an analog electronic circuit.

Main Results:

Related Experiment Videos

  • Chaos in the Lorenz system can be suppressed by high-frequency periodic or stochastic parametric forces.
  • Derived theoretical criteria for chaos suppression show good agreement with simulations and experiments.

    • Conclusions:

    • High-frequency parametric forcing is an effective method for controlling chaos in the Lorenz system.
    • The study provides a validated theoretical framework for chaos suppression.