Stochastic multiresonance and correlation-time-controlled stability for a harmonic oscillator with fluctuating frequency

Mankin, Romi; Laas, Katrin; Laas, T.; Reiter, Eerik

doi:10.1103/physreve.78.031120

Cited by 68 publications

(34 citation statements)

References 37 publications

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“…In Figure 2 several graphs depict the behavior of SPA versus a 2 for different representative values of the system parameters. These graphs show a typical resonance-like behavior of A 2 (a), i.e., a SR phenomenon appears at increase in a [33]. The existence of such an SR effect depends strongly on other system parameters.…”

Section: Stochastic Resonancementioning

confidence: 83%

Resonant behavior of a fractional oscillator with fluctuating mass

Sauga¹,

Mankin²,

Ainsaar³

2012

AIP Conference Proceedings

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We examine the phenomenon of stochastic resonance of a fractional oscillator that has a random mass and is subject to an external periodic force. The colored fluctuations of the oscillator mass are modeled as a dichotomous noise. The viscoelastic type friction kernel with memory is assumed as a power law function in time. An exact formula for the complex susceptibility of the oscillator is derived, and the dependence of the spectral amplification on system parameters is investigated. It is established that in certain regions of the system parameters an interplay of multiplicative noise and memory can generate a bona fide multiresonance versus the driving frequency as well as stochastic resonance vs noise parameters. Influence of the memory exponent in the resonance regimes of the oscillator is also investigated. Particularly, it is shown that the results about stochastic resonance in the model considered are significantly different from recently obtained results for fractional oscillators with fluctuating frequency and with fluctuating damping.

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Section: Stochastic Resonancementioning

confidence: 83%

Resonant behavior of a fractional oscillator with fluctuating mass

Sauga¹,

Mankin²,

Ainsaar³

2012

AIP Conference Proceedings

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“…1), the trichotomically switching mass m(t) = 1 + ξ(t) switches very slowly which yields three resonance peaks at three different frequencies depending on {−a, 0, a} of ξ(t). When the correlation rate v increases, the positions of the three peaks shift together [41]. In addition, these three resonance peaks appear at the frequencies…”

Section: The Bona Fide Stochastic Resonancementioning

confidence: 93%

Trichotomous Noise Induced Resonance Behavior for a Fractional Oscillator with Random Mass

Zhong

Gao

2015

J Stat Phys

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We investigate the stochastic resonance (SR) phenomenon in a fractional oscillator with random mass under the external periodic force. The fluctuations of the mass are modeled as a trichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform technique, we obtain the exact expression of the first moment of the system. The non-monotonic behaviors of the spectral amplification (SPA) versus the driving frequency indicate that the bona fide SR appears. The necessary and sufficient conditions for the emergence of the generalized stochastic resonance phenomena on the noise flatness and on the noise intensity in the particular case of = ω 0 , v → 0 are established. Particularly, the hypersensitive response of the SPA to the noise intensity is found, which is previously reported and believed to be absent in the case of dichotomous noise.

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“…with P = 2π/Ω, and the output SNR [24,25]. According to [24], the output SNR (R) is defined in terms of the Fourier cosine transform of the coherent and incoherent parts of the average of the two-time correlation function…”

Section: Model and The Output Characteristicsmentioning

confidence: 99%