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The resonance behavior in the fractional harmonic oscillator with time delay and fluctuating mass

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

Abstract

We study stochastic resonance (SR) in a fractional harmonic oscillator with time delay and mass fluctuation. Using a moment equation, we derive the exact analytical expression of the output amplitude and find that fluctuations in the output amplitude are nonmonotonic. Using numerical simulations we verify the accuracy of the analytical result. We find (i) that the evolution of output amplitude versus the frequency of the external periodic force exhibits One-Peak SR and Two-Peaks SR, resonance region and resonance form largely depend on the noise correlation rate and noise intensity, (ii) that the evolution of output amplitude versus the noise intensity exhibits One-Peak SR and the increasing time delay lower the critical driving frequency, and (iii) that the evolution of output amplitude versus feedback gain performs diverse resonance forms, the increasing time delay widens the region for occurrence of SR and diversifies the resonance form.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320801
    DOI: 10.1016/j.physa.2019.123731
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    References listed on IDEAS

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    1. Guo, Feng & Zhu, Cheng-Yin & Cheng, Xiao-Feng & Li, Heng, 2016. "Stochastic resonance in a fractional harmonic oscillator subject to random mass and signal-modulated noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 86-91.
    2. Gitterman, M., 2014. "Stochastic oscillator with random mass: New type of Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 11-21.
    3. Shapiro, V.E. & Loginov, V.M., 1978. "“Formulae of differentiation” and their use for solving stochastic equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 563-574.
    4. Wang, Huiqi & Ni, Feixiang & Lin, Lifeng & Lv, Wangyong & Zhu, Hongqiang, 2018. "Transport behaviors of locally fractional coupled Brownian motors with fluctuating interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 124-135.
    5. Ren, Ruibin & Deng, Ke, 2019. "Noise and periodic signal induced stochastic resonance in a Langevin equation with random mass and frequency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 145-155.
    6. 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.
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    1. 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).

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