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Parametric autoresonance.

E Khain1, B Meerson

  • 1Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
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Parametric autoresonance, a sustained phase lock in nonlinear oscillators with slowly changing driving frequencies, allows continuous resonant excitation. This study analyzes the phenomenon using averaging and adiabatic invariants.

Area of Science:

  • Nonlinear Dynamics
  • Oscillations and Waves
  • Theoretical Physics

Background:

  • Nonlinear oscillators exhibit complex behaviors under external forcing.
  • Parametric excitation can lead to resonance, but nonlinearity often limits amplitude.
  • Slowly varying driving frequencies introduce unique dynamics not captured by steady-state analysis.

Purpose of the Study:

  • To investigate parametric autoresonance in nonlinear oscillators.
  • To understand the mechanism of persisting phase locking under slowly varying driving frequencies.
  • To analyze the conditions under which resonant excitation remains unarrested by nonlinearity.

Main Methods:

  • Averaging over the fastest time scale of the oscillator.
  • Analytical analysis of the reduced equations.

Related Experiment Videos

  • Numerical simulations of the system dynamics.
  • Exploiting scale separation and adiabatic invariants for analytical solutions.

    • Main Results:

    • Identified parametric autoresonance as a phenomenon of persistent phase locking.
    • Demonstrated continuous and unarrested resonant excitation in this regime.
    • Derived analytical results using averaging and adiabatic invariants, supported by numerical analysis.
    • Showcased the importance of scale separation in analyzing the system.

    Conclusions:

    • Parametric autoresonance provides a mechanism for sustained resonant energy transfer in nonlinear systems.
    • The study offers a robust analytical framework for understanding this phenomenon.
    • Findings have implications for controlling and predicting the behavior of nonlinear oscillators in time-varying environments.