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Attractor selection in chaotic dynamics.

R Meucci1, E Allaria, F Salvadori

  • 1Istituto Nazionale di Ottica Applicata, Largo E. Fermi, 5 50125 Firenze, Italy.

Physical Review Letters
|December 31, 2005
PubMed
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This study introduces a novel control method to suppress chaotic amplitude jumps in bistable systems. The technique filters specific frequencies, effectively stabilizing dynamics in both model and experimental CO2 laser systems.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Experimental Physics

Background:

  • Chaotic systems exhibit complex behaviors, including generalized bistability with two stable attractors.
  • System dynamics can transition to a crisis, where chaotic attractors collide with unstable orbits, leading to amplitude jumps.
  • Jumps in bistable regimes are typically triggered by external perturbations, while crisis-induced jumps manifest as random bursts.

Purpose of the Study:

  • To develop and validate a control method for suppressing chaotic amplitude jumps.
  • To address jump phenomena in both generalized bistability and crisis regimes.
  • To demonstrate the method's efficacy in both theoretical models and experimental setups.

Main Methods:

  • A control strategy based on filtering specific frequency content of dynamical objects was introduced.

Related Experiment Videos

  • The method was tested on a mathematical model exhibiting chaotic dynamics.
  • The technique was experimentally validated using a CO2 laser system.

    • Main Results:

    • The proposed control method successfully suppressed amplitude jumps in both generalized bistability and crisis scenarios.
    • Filtering specific frequencies effectively stabilized the chaotic system's dynamics.
    • Consistent results were observed between the model simulations and the CO2 laser experiment.

    Conclusions:

    • Frequency filtering is an effective method for controlling chaotic amplitude jumps.
    • This approach offers a viable strategy for stabilizing complex dynamical systems.
    • The demonstrated method has practical implications for systems exhibiting bistability and chaotic crises.