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Optimized chaos control with simple limiters.

C Wagner1, R Stoop

  • 1Institute of Pharmacology, University of Bern, Friedbuehlstrasse 49, CH-3010 Bern, Switzerland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 17, 2001
PubMed
Summary
This summary is machine-generated.

This study introduces simple limiters for chaos control, offering conditions to stabilize unstable periodic orbits in chaotic systems like the logistic and Henon maps.

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Area of Science:

  • Nonlinear dynamics
  • Chaos theory

Background:

  • Chaotic systems exhibit complex, unpredictable behavior.
  • Stabilizing unstable periodic orbits is crucial for controlling chaos.

Purpose of the Study:

  • To present an elementary derivation for chaos control using simple limiters.
  • To provide conditions for optimal stabilization of unstable periodic orbits.

Main Methods:

  • Utilized the logistic map and the Henon map as model systems.
  • Developed a derivation based on simple limiter functions.

Main Results:

  • Demonstrated an accessible method for chaos control.
  • Identified specific conditions for stabilizing chaotic dynamics.

Conclusions:

  • The proposed method offers a straightforward approach to controlling chaos.
  • The derived conditions enable precise stabilization of chaotic attractors.