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Phase control of intermittency in dynamical systems.

Samuel Zambrano1, Inés P Mariño, Francesco Salvadori

  • 1Nonlinear Dynamics and Chaos Group, Departamento de Ciencias de la Naturaleza y Física Aplicada, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2006
PubMed
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A new nonfeedback method uses harmonic perturbation to control crisis-induced intermittency in dynamical systems. Phase differences in the perturbation allow for suppression or enhancement of intermittent behavior, demonstrated in models and laser experiments.

Area of Science:

  • Nonlinear Dynamics
  • Laser Physics

Background:

  • Dynamical systems can exhibit crisis-induced intermittency, a complex behavior where the system switches between different states.
  • Controlling such intermittent behavior is crucial for understanding and utilizing nonlinear systems.

Purpose of the Study:

  • To introduce a novel nonfeedback method for controlling crisis-induced intermittency.
  • To demonstrate the effectiveness of this method in both theoretical models and experimental setups.
  • To explore the role of phase control in manipulating intermittent dynamics.

Main Methods:

  • Applying a small harmonic perturbation to a system parameter.
  • Investigating the effect of the phase difference between the main driving force and the perturbation.
  • Validating the method using a mathematical model (quadratic map) and a physical experiment (CO2 laser).

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Main Results:

  • The harmonic perturbation can effectively suppress or enhance intermittency.
  • The outcome (suppression or enhancement) is dependent on the phase difference of the perturbation.
  • The method's validity is confirmed through both numerical simulations and experimental data.

Conclusions:

  • A simple, nonfeedback method can precisely control crisis-induced intermittency in nonlinear systems.
  • Phase control is a key factor in manipulating complex dynamics near crises.
  • This technique offers a new approach for managing unpredictable behavior in dynamical systems.