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Controlling chaos in unidimensional maps using macroevolutionary algorithms.

Jesús Marín1, Ricard V Solé

  • 1E. U. d'Enginyers Tècnics Industrials de Barcelona, Department of Automatic Control, Technical University of Catalonia, Compte d'Urgell, 187, 08036 Barcelona, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
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We present a new search algorithm for chaos control in discrete maps. This method efficiently finds desired orbits by exploring system parameters, even for complex periodic behaviors.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Computational Physics

Background:

  • Discrete maps are fundamental models in nonlinear dynamics.
  • Chaos control aims to stabilize unstable periodic orbits within chaotic systems.
  • Existing methods can be computationally intensive for parameter exploration.

Purpose of the Study:

  • To introduce a novel, simple search algorithm for chaos control.
  • To efficiently explore parameter space for periodically perturbed discrete maps.
  • To find desired orbits and high-fitness solutions in chaotic systems.

Main Methods:

  • The algorithm explores the parameter space of periodically perturbed discrete maps.
  • It is applied to one-dimensional maps and is extendable to higher dimensions.

Related Experiment Videos

  • Two chaos control types are considered: proportional pulses and constant feedback.

    • Main Results:

    • The method enables rapid exploration of the parameter space.
    • It successfully identifies high-fitness solutions close to target orbits.
    • The algorithm is effective even for high periodicities.

    Conclusions:

    • The developed search algorithm offers an efficient approach to chaos control.
    • It provides a practical tool for finding desired orbits in complex dynamical systems.
    • The method's extendibility to higher dimensions broadens its applicability.