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Controlling oscillator coherence by delayed feedback.

D Goldobin1, M Rosenblum, A Pikovsky

  • 1Department of Physics, University of Potsdam, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
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Delayed feedback effectively controls the coherence of noisy oscillators. This study develops a theory and shows good agreement with numerical simulations for synchronization control applications.

Area of Science:

  • Nonlinear dynamics
  • Control theory
  • Statistical physics

Background:

  • Self-sustained oscillators are fundamental in various scientific fields.
  • Noise and chaos can degrade oscillator coherence, limiting applications.
  • Controlling oscillator behavior is crucial for signal processing and system synchronization.

Purpose of the Study:

  • To demonstrate and theoretically explain the control of oscillator coherence using delayed feedback.
  • To develop a mathematical framework for understanding this control mechanism.
  • To explore potential applications in synchronization control.

Main Methods:

  • Development of a theoretical model for noisy oscillators under delayed feedback.
  • Application of the Gaussian approximation for system analysis.

Related Experiment Videos

  • Derivation of closed-form equations for phase diffusion and mean frequency.
  • Numerical simulations to validate theoretical predictions.

    • Main Results:

    • Delayed feedback significantly enhances the coherence of noisy or chaotic self-sustained oscillators.
    • The developed theory accurately predicts system behavior for weak feedback and strong noise.
    • The phase diffusion constant and mean frequency were successfully modeled.

    Conclusions:

    • Delayed feedback offers an efficient method for controlling oscillator coherence.
    • The theoretical framework provides valuable insights into noise-induced phenomena in oscillators.
    • This control strategy has potential applications in achieving robust synchronization in complex systems.