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Scaling properties of simple limiter control.

R Stoop1, C Wagner

  • 1Institute of Neuroinformatics, ETHZ/UNIZH, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland.

Physical Review Letters
|May 7, 2003
PubMed
Summary

Simple limiter control stabilizes chaotic systems efficiently. This method ensures exponential orbit stabilization, regardless of system periodicity, and is highly effective in higher dimensions with proper configuration.

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Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Control theory

Background:

  • Chaotic systems exhibit unpredictable behavior.
  • Controlling chaos is crucial for scientific and engineering applications.
  • Simple limiter control offers a potential method for chaos management.

Purpose of the Study:

  • To analytically and numerically investigate the properties of simple limiter control.
  • To describe the control method using the one-dimensional flat-top map family.
  • To assess the efficiency of simple limiter control in higher dimensions.

Main Methods:

  • Analytical investigation of chaotic systems.
  • Numerical simulations using the one-dimensional flat-top map family.
  • Exploration of control parameter space and its scaling properties.

Main Results:

  • Orbits are stabilized in exponential time, independent of periodicity.
  • Control effectiveness is limited by superexponential scaling in control space.
  • Simple limiter control proves highly efficient in higher dimensions when properly configured.

Conclusions:

  • Simple limiter control is a robust method for stabilizing chaotic systems.
  • The one-dimensional flat-top map family fully characterizes the control properties.
  • Optimal limiter form and placement are key for high-dimensional chaos control.

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