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Mittag-Leffler noise induced stochastic resonance in a generalized Langevin equation with random inherent frequency

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  • He, Guitian
  • Guo, Dali
  • Tian, Yan
  • Li, Tiejun
  • Luo, Maokang

Abstract

The generalized stochastic resonance (GSR) and the bona fide stochastic resonance (SR) in a generalized Langevin equation driven by a periodic signal, multiplicative noise and Mittag-Leffler noise are extensively investigated. The expression of the frequency spectrum of the Mittag-Leffler noise is studied. Using the Shapiro–Loginov formula and Laplace transformation technique, the exact expressions of the output amplitude gain and the signal-to-noise ratio are obtained. The simulation results turn out that the output amplitude gain and the signal-to-noise ratio are non-monotonic functions of the characteristics of noise parameters and system parameters. Especially, the influence of the memory exponent and memory time of Mittag-Leffler noise could induce the GSR phenomenon. The influence of the driving frequency could induce the bona fide stochastic resonance. It is found that the system with fractional memory exponent could be more easily induced SR phenomenon than the system with integer memory exponent.

Suggested Citation

  • He, Guitian & Guo, Dali & Tian, Yan & Li, Tiejun & Luo, Maokang, 2017. "Mittag-Leffler noise induced stochastic resonance in a generalized Langevin equation with random inherent frequency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 91-103.
    • Handle: RePEc:eee:phsmap:v:484:y:2017:i:c:p:91-103
    DOI: 10.1016/j.physa.2017.04.153
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    Cited by:

    1. Zhang, Ruoqi & Meng, Lin & Yu, Lei & Shi, Sihong & Wang, Huiqi, 2024. "Collective dynamics of fluctuating–damping coupled oscillators in network structures: Stability, synchronism, and resonant behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).
    2. Hollerbach, Rainer & Kim, Eun-jin & Mahi, Yanis, 2019. "Information length as a new diagnostic in the periodically modulated double-well model of stochastic resonance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1313-1322.
    3. Tian, Yan & He, Guitian & Liu, Zhibin & Zhong, Linfeng & Yang, Xinping & Stanley, H. Eugene & Tu, Zhe, 2021. "The impact of memory effect on resonance behavior in a fractional oscillator with small time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    4. Lini Qiu & Guitian He & Yun Peng & Huijun Lv & Yujie Tang, 2023. "Average amplitudes analysis for a phenomenological model under hydrodynamic interactions with periodic perturbation and multiplicative trichotomous noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(4), pages 1-20, April.

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