IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v669y2025ics037843712500233x.html
   My bibliography  Save this article

Generalized stochastic resonance of the harmonic oscillator with Mittag–Leffler memory kernel and time delay

Author

Listed:
  • Tian, Yan

Abstract

In this study, we introduce a fluctuating-mass harmonic oscillator with Mittag-Leffler memory kernel and time delay. Firstly, we derive the exact analytical expression of output amplitude gain (OAG) using moment method. Then, we observe the generalized stochastic resonance (GSR) in the system based on the expression. We further examine how GSR behavior depends on system parameters, and discuss the similarities and differences of GSR behavior between Mittag-Leffler memory kernel and classical power-law memory kernel. We demonstrate time delay, the characteristic memory time and the memory exponent are crucial in facilitating its resonance form and optimizing its intensity. In particular, the resonance intensity could quickly enhanced by tuning the above parameters, which has important application in some fields such as signal detection. Finally, we verify the accuracy of the analytical result using numerical simulations.

Suggested Citation

  • Tian, Yan, 2025. "Generalized stochastic resonance of the harmonic oscillator with Mittag–Leffler memory kernel and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 669(C).
    • Handle: RePEc:eee:phsmap:v:669:y:2025:i:c:s037843712500233x
    DOI: 10.1016/j.physa.2025.130581
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843712500233X
    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.2025.130581?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Peng, Jian & Li, Yanan & Li, Luxin & Lenci, Stefano & Sun, Hongxin, 2024. "Time-delay feedback control of a suspended cable driven by subharmonic and superharmonic resonance," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Du, Yuru & Meng, Lin & Lin, Lifeng & Wang, Huiqi, 2024. "Resonant behaviors of two coupled fluctuating-frequency oscillators with tempered Mittag-Leffler memory kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    3. Zhang, Yufeng & Li, Jing & Zhu, Shaotao & Ma, Zerui, 2024. "Harmonic resonance and bifurcation of fractional Rayleigh oscillator with distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 281-297.
    4. 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.
    5. Liemert, André & Sandev, Trifce & Kantz, Holger, 2017. "Generalized Langevin equation with tempered memory kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 356-369.
    6. 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).
    7. Zhao, Dazhi & Luo, Maokang, 2019. "Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 531-544.
    8. 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).
    9. Hilfer, R., 2003. "On fractional diffusion and continuous time random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 35-40.
    Full references (including those not matched with items on IDEAS)

    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. 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).
    2. 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).
    3. Zhao, Yongqiang & Tang, Yanbin, 2024. "Critical behavior of a semilinear time fractional diffusion equation with forcing term depending on time and space," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Zhao, Dazhi & Yu, Guozhu & Tian, Yan, 2020. "Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    5. Shiri, Babak & Baleanu, Dumitru, 2023. "All linear fractional derivatives with power functions’ convolution kernel and interpolation properties," Chaos, Solitons & Fractals, Elsevier, vol. 170(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. 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).
    8. Muhammad Samraiz & Ahsan Mehmood & Saima Naheed & Gauhar Rahman & Artion Kashuri & Kamsing Nonlaopon, 2022. "On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function," Mathematics, MDPI, vol. 10(21), pages 1-19, October.
    9. Wei, Dongmei & Liu, Hailing & Li, Yongmei & Wan, Linchun & Qin, Sujuan & Wen, Qiaoyan & Gao, Fei, 2024. "Non-Markovian dynamics of time-fractional open quantum systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    10. El-Nabulsi, Rami Ahmad & Anukool, Waranont, 2025. "Modeling stochastic Langevin dynamics in fractal dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 667(C).
    11. Gorenflo, Rudolf & Mainardi, Francesco & Vivoli, Alessandro, 2007. "Continuous-time random walk and parametric subordination in fractional diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 87-103.
    12. Rodríguez, R.F. & Gomez-Solano, J.R. & Fujioka, J., 2025. "Active diffusion model and dynamic structure factor of self-propelled particles in a three parameters fluctuating Mittag-Leffler fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 662(C).
    13. Sandev, Trifce & Sokolov, Igor M. & Metzler, Ralf & Chechkin, Aleksei, 2017. "Beyond monofractional kinetics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 210-217.
    14. Allahviranloo, T. & Gouyandeh, Z. & Armand, A., 2015. "Numerical solutions for fractional differential equations by Tau-Collocation method," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 979-990.
    15. Zu, Chuanjin & Gao, Yanming & Yu, Xiangyang, 2021. "Time fractional evolution of a single quantum state and entangled state," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    16. Gafiychuk, V.V. & Datsko, B.Yo., 2006. "Pattern formation in a fractional reaction–diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 300-306.
    17. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
    18. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    19. Lu, Xin & Chen, Ning & Li, Hui & Guo, Shiyu & Chen, Zengtao, 2023. "Simulation of the temperature distribution of lithium-ion battery module considering the time-delay effect of the porous electrodes," Energy, Elsevier, vol. 284(C).
    20. Zhao, Dazhi & Luo, Maokang, 2019. "Supplementary remark to ‘Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds’ [Applied Mathem," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 175-176.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:669:y:2025:i:c:s037843712500233x. 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.