Trichotomous noise induced resonance behavior for a fractional oscillator with random mass.

*(English)*Zbl 1396.70026Summary: 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 \(\Omega =\omega_0\), \(v\to 0\) 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.

##### MSC:

70L05 | Random vibrations in mechanics of particles and systems |

60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |

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\textit{S. Zhong} et al., J. Stat. Phys. 159, No. 1, 195--209 (2015; Zbl 1396.70026)

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