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Related Experiment Videos

Open-loop sustained chaos and control: a manifold approach.

Ira B Schwartz1, Ioana Triandaf, Riccardo Meucci

  • 1Nonlinear System Dynamics Section, U.S. Naval Research Laboratory, Code 6792, Plasma Physics Division, Washington, D.C. 20375-5000, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary

This study introduces multifrequency phase control to maintain chaotic behavior in stable systems and periodic behavior in chaotic systems. This method manipulates manifold intersections for precise control of nonlinear dynamics.

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Area of Science:

  • Nonlinear Dynamics and Control
  • Laser Physics

Background:

  • Nonlinear systems driven at a base frequency can exhibit complex behaviors like chaos.
  • Controlling these behaviors, especially in postcrisis regimes, remains a challenge.

Purpose of the Study:

  • To present a general method for preserving chaos in nonchaotic regimes and periodic behavior in chaotic regimes.
  • To demonstrate the manipulation of stable and unstable manifold intersections.

Main Methods:

  • Introduction of multifrequency phase control, involving subharmonic amplitude modulation and phase shift.
  • Application to nonlinear systems driven at a base frequency.
  • Theoretical development and preliminary experimental validation.

Main Results:

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  • Successfully preserved chaos in nonchaotic parameter regimes.
  • Successfully preserved periodic behavior in chaotic regimes.
  • Demonstrated manipulation of manifold intersections to sustain desired dynamics.

Conclusions:

  • Multifrequency phase control offers a versatile approach to stabilize or destabilize nonlinear system dynamics.
  • The method is effective for controlling complex behaviors in driven nonlinear systems.
  • Validated through theoretical analysis and experiments on a CO2 laser.