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Harmonic oscillator with fluctuating damping parameter.

M Gitterman1

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan, 52900 Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 1, 2004
PubMed
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Multiplicative noise in harmonic oscillators can cause instability. Stochastic resonance, observed with external forces, shows a nonmonotonic signal dependence on noise, occurring for both color and white noise.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Harmonic oscillators are fundamental systems in physics.
  • Fluctuating parameters introduce complex dynamics.
  • Multiplicative noise effects on oscillators are not fully understood.

Purpose of the Study:

  • To investigate the impact of multiplicative noise on an underdamped harmonic oscillator.
  • To analyze the role of noise strength and rate in oscillator behavior.
  • To explore the phenomenon of stochastic resonance in this system.

Main Methods:

  • Theoretical analysis of the oscillator's equation of motion.
  • Inclusion of multiplicative noise from a fluctuating damping parameter.
  • Examination of the average coordinate and output signal under external periodic force.

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Main Results:

  • Multiplicative noise can induce instability in the oscillator.
  • A nonmonotonic dependence of the output signal on noise strength and rate is observed.
  • Stochastic resonance occurs for both color and white noise, unlike random frequency cases.

Conclusions:

  • Fluctuating damping parameters significantly alter oscillator dynamics.
  • The system exhibits stochastic resonance, a key nonlinear phenomenon.
  • The presence of stochastic resonance for white noise broadens its applicability.