IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v545y2020ics0378437119320801.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119320801
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123731?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    4. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Lin, Lifeng & Lin, Tianzhen & Zhang, Ruoqi & Wang, Huiqi, 2023. "Generalized stochastic resonance in a time-delay fractional oscillator with damping fluctuation and signal-modulated noise," Chaos, Solitons & Fractals, Elsevier, vol. 170(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. 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).
    6. 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.
    7. Taiwo O. Roy-Layinde & Kehinde A. Omoteso & Babatunde A. Oyero & John A. Laoye & Uchechukwu E. Vincent, 2022. "Vibrational resonance of ammonia molecule with doubly singular position-dependent mass," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(5), pages 1-11, May.
    8. Chen, Xi & Luo, Maokang & Zhong, Yangfan & Zhang, Lu, 2022. "Collective dynamic behaviors of a general adjacent coupled chain in both unconfined and confined spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    9. Fang, Yuwen & Luo, Yuhui & Zeng, Chunhua, 2022. "Dichotomous noise-induced negative mass and mobility of inertial Brownian particle," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. Jochen Jungeilges & Tatyana Ryazanova, 2018. "Output volatility and savings in a stochastic Goodwin economy," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 8(3), pages 355-380, December.
    11. 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).
    12. 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).
    13. Juan-Carlos Cortés & Elena López-Navarro & José-Vicente Romero & María-Dolores Roselló, 2021. "Approximating the Density of Random Differential Equations with Weak Nonlinearities via Perturbation Techniques," Mathematics, MDPI, vol. 9(3), pages 1-17, January.
    14. Cui, Yingxue & Ning, Lijuan, 2023. "Transport of coupled particles in fractional feedback ratchet driven by Bounded noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    15. 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.
    16. Lin, Lifeng & Wang, Huiqi & Ma, Hong, 2019. "Directed transport properties of double-headed molecular motors with balanced cargo," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 270-279.
    17. Zhang, Peng-Juan & Zhang, Ji-Qiang & Wang, Peng & Huo, Jie & Wang, Xu-Ming, 2024. "Directed transport of two-coupled particles under the coordination of the coupling and an asymmetric potential," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    18. Guo, Feng & Wang, Xue-yuan & Qin, Ming-wei & Luo, Xiang-dong & Wang, Jian-wei, 2021. "Resonance phenomenon for a nonlinear system with fractional derivative subject to multiplicative and additive noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    19. Guo, Feng & Wang, Xue-Yuan & Zhu, Cheng-Yin & Cheng, Xiao-Feng & Zhang, Zheng-Yu & Huang, Xu-Hui, 2017. "Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 205-214.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320801. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.