IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v561y2021ics0378437120306002.html
   My bibliography  Save this article

Stochastic resonance in two coupled fractional oscillators with potential and coupling parameters subjected to quadratic asymmetric dichotomous noise

Author

Listed:
  • Vishwamittar,
  • Batra, Priyanka
  • Chopra, Ribhu

Abstract

Exact analytical expressions for the average output amplitude gains in the very long-time limit for two coupled oscillators governed by fractional-order intrinsic and external damping, under the influence of a multiplicative quadratic asymmetric dichotomous noise affecting the two potential parameters and the coupling factors, and subjected to a noise-free or noise-modulated external periodic force with same frequency, have been derived. The trustworthiness of the analytical expressions has been checked by comparing the numerical results obtained using these for some typical cases with corresponding findings based on numerical simulations. The numerical simulations have also been used to investigate the time-evolution of a representative system in the transient state by studying the probability density and displacements of the two oscillators at different times and for different values of noise intensity. Analytical expressions have been used to obtain plots for gains versus noise intensity to study the effect of (i) variation in mass parameter of one oscillator keeping that of other the same, and (ii) change in the relative values of the two coupling coefficients. Furthermore, the special case where both the potential parameters are taken to be zero, which corresponds to rectilinear motion of the two particles in the absence of fluctuations, has been examined under the influence of the second-order noise and stochastic resonance has been found to occur at lower frequencies of the applied force. This highlights the importance of nonlinear term in the noise, which makes the rectilinear motion to be oscillatory. Also, the key role played by the coupling in this has been brought out.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:561:y:2021:i:c:s0378437120306002
    DOI: 10.1016/j.physa.2020.125148
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120306002
    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.2020.125148?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. Spagnolo, B. & Valenti, D. & Guarcello, C. & Carollo, A. & Persano Adorno, D. & Spezia, S. & Pizzolato, N. & Di Paola, B., 2015. "Noise-induced effects in nonlinear relaxation of condensed matter systems," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 412-424.
    2. 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.
    3. Tofighi, Ali, 2003. "The intrinsic damping of the fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 29-34.
    4. 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.
    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. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    7. Suchuan Zhong & Kun Wei & Lu Zhang & Hong Ma & Maokang Luo, 2016. "The Stochastic Resonance Behaviors of a Generalized Harmonic Oscillator Subject to Multiplicative and Periodically Modulated Noises," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-12, December.
    8. La Barbera, A & Spagnolo, B, 2002. "Spatio-temporal patterns in population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 120-124.
    9. Jiang, Shiqi & Guo, Feng & Zhou, Yurong & Gu, Tianxiang, 2007. "Parameter-induced stochastic resonance in an over-damped linear system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 483-491.
    10. 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.
    11. Zhang, Gang & Shi, Jiabei & Zhang, Tianqi, 2018. "Stochastic resonance in an under-damped linear system with nonlinear frequency fluctuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 230-240.
    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. Qiao, Zijian & He, Yuanbiao & Liao, Changrong & Zhu, Ronghua, 2023. "Noise-boosted weak signal detection in fractional nonlinear systems enhanced by increasing potential-well width and its application to mechanical fault diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Zhang, Gang & Liu, Xiaoman & Zhang, Tianqi, 2022. "Two-Dimensional Tri-stable Stochastic Resonance system and its application in bearing fault detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    3. 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.

    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 & 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. 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).
    3. 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).
    4. Xu, Pengfei & Jin, Yanfei, 2020. "Coherence and stochastic resonance in a second-order asymmetric tri-stable system with memory effects," Chaos, Solitons & Fractals, Elsevier, vol. 138(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. Jin, Yanfei & Wang, Heqiang, 2020. "Noise-induced dynamics in a Josephson junction driven by trichotomous noises," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    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. Wang, Yupin & Liu, Shutang & Li, Hui & Wang, Da, 2019. "On the spatial Julia set generated by fractional Lotka-Volterra system with noise," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 129-138.
    9. Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    10. Wu, Anshun & Dong, Yang & Luo, Yuhui & Zeng, Chunhua, 2020. "Fluctuations-induced regime shifts in the Endogenous Credit system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    11. Zhang, Hongxia & Xu, Wei & Guo, Qin & Han, Ping & Qiao, Yan, 2020. "First escape probability and mean first exit time for a time-delayed ecosystem driven by non-Gaussian colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    12. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2020. "Analysis of regular and chaotic dynamics in a stochastic eco-epidemiological model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    13. Dong, Haitao & Shen, Xiaohong & He, Ke & Wang, Haiyan, 2020. "Nonlinear filtering effects of intrawell matched stochastic resonance with barrier constrainted duffing system for ship radiated line signature extraction," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Bashkirtseva, Irina & Perevalova, Tatyana & Ryashko, Lev, 2020. "Noise-induced shifts in dynamics of multi-rhythmic population SIP-model," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    15. Shi, Zhuozheng & Liao, Zhiqiang & Tabata, Hitoshi, 2022. "Boosting learning ability of overdamped bistable stochastic resonance system based physical reservoir computing model by time-delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    16. Rao, Feng & Wang, Weiming & Li, Zhenqing, 2009. "Spatiotemporal complexity of a predator–prey system with the effect of noise and external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1634-1644.
    17. Jiang, Wei & Chen, Zhong & Hu, Ning & Song, Haiyang & Yang, Zhaohong, 2020. "Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    18. Raja Sekhara Rao, P. & Naresh Kumar, M., 2015. "A dynamic model for infectious diseases: The role of vaccination and treatment," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 34-49.
    19. Fang, Yuwen & Luo, Yuhui & Ma, Zhiqing & Zeng, Chunhua, 2021. "Transport and diffusion in the Schweitzer–Ebeling–Tilch model driven by cross-correlated noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
    20. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2019. "Stochastic variability and transitions to chaos in a hierarchical three-species population model," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 276-283.

    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:561:y:2021:i:c:s0378437120306002. 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.