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

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Abstract

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 \(\Omega =\omega _0 ,v\rightarrow 0\) 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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Acknowledgments

This work was supported by the Key Program of National Natural Science Foundation of China (Grant number 11171238) and the Young Teacher Fund of Sichuan Uninversity, China (Grant number 2082604174031).

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Authors and Affiliations

  1. College of Aeronautics and Astronautics, Sichuan University, Chengdu, 610065, China

    Suchuan Zhong

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Kun Wei

  3. College of Mathematics and Information Science, Leshan Normal University, Leshan, 614000, China

    Shilong Gao

  4. College of Mathematics, Sichuan University, Chengdu, 610065, China

    Hong Ma

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  1. Suchuan Zhong
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  4. Hong Ma
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Correspondence to Suchuan Zhong or Hong Ma.

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Zhong, S., Wei, K., Gao, S. et al. Trichotomous Noise Induced Resonance Behavior for a Fractional Oscillator with Random Mass. J Stat Phys 159, 195–209 (2015). https://doi.org/10.1007/s10955-014-1182-9

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  • DOI: https://doi.org/10.1007/s10955-014-1182-9

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