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Stochastic Resonance in a Fractional Oscillator with Random Mass and Random Frequency

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Abstract

For a fractional linear oscillator subjected to two multiplicative dichotomous noises and a additive fractional Gaussian noise and driven by a periodic signal, we study the stochastic resonance (SR) in this paper. Using (fractional) Shapiro–Loginov formula and the Laplace transformation technique, we acquire the exact expression of the first-order moment of the system’s steady response. Meanwhile, we discuss the evolutions of the output amplitude with frequency of the periodic signal, noise parameters, fractional order, and friction coefficient. We find that SR in the wide sense existing in this system. Specially, the evolution of the output amplitude with frequency of the periodic signal presents one-peak oscillation and two-peak oscillation. Moreover, the friction coefficient can induce stochastic multi-resonance.

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Acknowledgments

This work was supported by the Science and Technology Project of the Education Department of Fujian Province (Grant No. JA14112), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20120181120089) and the National Natural Science Foundation of China (Grant No. 11301360).

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Correspondence to Li-Feng Lin or Hui-Qi Wang.

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Lin, LF., Chen, C., Zhong, SC. et al. Stochastic Resonance in a Fractional Oscillator with Random Mass and Random Frequency. J Stat Phys 160, 497–511 (2015). https://doi.org/10.1007/s10955-015-1265-2

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  • DOI: https://doi.org/10.1007/s10955-015-1265-2

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