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The resonant behavior in the oscillator with double fractional-order damping under the action of nonlinear multiplicative noise

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  • Tian, Yan
  • Zhong, Lin-Feng
  • He, Gui-Tian
  • Yu, Tao
  • Luo, Mao-Kang
  • Stanley, H. Eugene

Abstract

We study stochastic resonance (SR) in an oscillator with nonlinear noise, fractional-order external damping, and fractional-order intrinsic damping. Using a moment equation, we derive the exact analytical expression of the output amplitude and find that fluctuations in the output amplitude are non-monotonic. Using numerical simulations we verify the accuracy of this analytical result. We find (i) that nonlinear noise plays a key role in system behavior and that the resonance of the output amplitude is diverse when there is nonlinear noise, (ii) that the order of the fractional-order damping strongly impacts resonant intensity and that the impact on resonant intensity of fractional-order external damping is opposite that of fractional-order intrinsic damping, and (iii) that the evolution of the output amplitude versus the frequency of the external periodic force exhibits three behaviors: a resonance with one peak, a resonance with one peak and one valley, and a resonance with one valley.

Suggested Citation

  • Tian, Yan & Zhong, Lin-Feng & He, Gui-Tian & Yu, Tao & Luo, Mao-Kang & Stanley, H. Eugene, 2018. "The resonant behavior in the oscillator with double fractional-order damping under the action of nonlinear multiplicative noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 845-856.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:845-856
    DOI: 10.1016/j.physa.2017.08.051
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    References listed on IDEAS

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    1. Tofighi, Ali, 2003. "The intrinsic damping of the fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 29-34.
    2. Narahari Achar, B.N. & Hanneken, John W. & Clarke, T., 2002. "Response characteristics of a fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 275-288.
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    Cited by:

    1. Tian, Yan & Yu, Tao & He, Gui-Tian & Zhong, Lin-Feng & Stanley, H. Eugene, 2020. "The resonance behavior in the fractional harmonic oscillator with time delay and fluctuating mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. 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).
    3. He, Lifang & Wu, Xia & Zhang, Gang, 2020. "Stochastic resonance in coupled fractional-order linear harmonic oscillators with damping fluctuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Lin, Lifeng & He, Minyue & Wang, Huiqi, 2022. "Collective resonant behaviors in two coupled fluctuating-mass oscillators with tempered Mittag-Leffler memory kernel," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. Vishwamittar, & Batra, Priyanka & Chopra, Ribhu, 2021. "Stochastic resonance in two coupled fractional oscillators with potential and coupling parameters subjected to quadratic asymmetric dichotomous noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    6. You, Pinlong & Lin, Lifeng & Wang, Huiqi, 2020. "Cooperative mechanism of generalized stochastic resonance in a time-delayed fractional oscillator with random fluctuations on both mass and damping," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

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