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Stochastic multiresonance and correlation-time-controlled stability for a harmonic oscillator with fluctuating
Romi Mankin1, Katrin Laas, Tõnu Laas
1Institute of Mathematics and Natural Sciences, Tallinn University, 25 Narva Road, 10120 Tallinn, Estonia.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
This study analyzes a harmonic oscillator with fluctuating frequency, finding that its stochastic resonance characteristics depend non-monotonically on noise and signal parameters. It reveals a link between energetic instability and stochastic multiresonance.
Area of Science:
- Nonlinear dynamics
- Statistical physics
- Complex systems
Background:
- Harmonic oscillators with fluctuating frequencies are crucial in various physical systems.
- Understanding stochastic resonance (SR) in such systems is key to signal processing and noise control.
- Colored noise effects on SR phenomena require detailed analytical investigation.
Purpose of the Study:
- To analytically investigate the long-time behavior of a harmonic oscillator with frequency fluctuations.
- To calculate exact expressions for stochastic resonance characteristics under specific noise conditions.
- To analyze the dependence of SR characteristics on noise parameters and identify conditions for energetic instability.
Main Methods:
- Analytical treatment of the first two moments and correlation function of the output signal.
- Modeling frequency fluctuations using a three-level Markovian noise process.
- Application of the Shapiro-Loginov formula for calculating SR characteristics.
Main Results:
- Exact expressions for spectral amplification, output signal variance, signal-to-noise ratio, and SR gain were derived.
- Nonmonotonic dependencies of SR characteristics on noise parameters and input signal frequency were observed.
- Multiresonancelike behavior in variance and signal-to-noise ratio as functions of noise correlation time was identified.
Conclusions:
- A connection between energetic instability and stochastic multiresonance was established.
- Hypersensitive responses of spectral amplification to noise amplitude variations were discussed.
- The study provides insights into complex noise-induced phenomena in nonlinear systems.
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