IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v346y2019icp352-362.html
   My bibliography  Save this article

Stochastic resonance in an underdamped triple-well potential system

Author

Listed:
  • Xu, Pengfei
  • Jin, Yanfei
  • Zhang, Yanxia

Abstract

In this paper, stochastic resonance (SR) in an underdamped triple-well potential system driven by Gaussian white noise and a parametric harmonic excitation is investigated. The analytical expressions of the output signal-to-noise ratio (SNR), together with the mean first-passage times (MFPTs), are derived for the triple-well potential system involving damping in adiabatic limit. The effects of noise intensity, damping coefficient and triple-well potential on MFPTs and SNR are analyzed. The results suggest the existence of two critical damping values, giving rise to the onset and the disappearance of SR, respectively. Since the system is unstable in weak damping regime, emergence of SR is prohibited. Under the weak noise level, SNR exhibits a prominent resonance-like behavior at the optimal value of damping coefficient. Moreover, the two nonlinear stiffness coefficients of restoring force play an opposite role in the enhancement of SR. Thus, the SR effect significantly depends on the change of the two-side potential wells. Particularly, the appropriate choice of triple-well potential function and damping coefficient can improve the response of the system to an external periodic excitation according to the damping-induced resonance effect. Finally, the numerical results confirm the effectiveness of the theoretical analyses.

Suggested Citation

  • Xu, Pengfei & Jin, Yanfei & Zhang, Yanxia, 2019. "Stochastic resonance in an underdamped triple-well potential system," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 352-362.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:352-362
    DOI: 10.1016/j.amc.2018.10.060
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318309263
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.10.060?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. Xu, Pengfei & Jin, Yanfei, 2018. "Mean first-passage time in a delayed tristable system driven by correlated multiplicative and additive white noises," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 75-82.
    2. Z. Jia & D. Mei, 2012. "Controlling the noise enhanced stability effect via noise recycling in a metastable system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(4), pages 1-8, April.
    3. Saikia, Shantu, 2014. "The role of damping on Stochastic Resonance in a periodic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 411-420.
    4. Xu, Pengfei & Jin, Yanfei, 2018. "Stochastic resonance in multi-stable coupled systems driven by two driving signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1281-1289.
    5. Yilmaz, Ergin & Uzuntarla, Muhammet & Ozer, Mahmut & Perc, Matjaž, 2013. "Stochastic resonance in hybrid scale-free neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5735-5741.
    6. Zhou, Shengxi & Cao, Junyi & Inman, Daniel J. & Lin, Jing & Liu, Shengsheng & Wang, Zezhou, 2014. "Broadband tristable energy harvester: Modeling and experiment verification," Applied Energy, Elsevier, vol. 133(C), pages 33-39.
    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, Wenyue & Shi, Peiming & Li, Mengdi & Han, Dongying, 2021. "A novel stochastic resonance model based on bistable stochastic pooling network and its application," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Zhang, Gang & Chen, Yezi & Xu, Lianbing, 2024. "Multi-dimensional hybrid potential stochastic resonance and application of bearing fault diagnosis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    3. Dongmei Huang & Shengxi Zhou & Zhichun Yang, 2019. "Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow-Band Stochastic Parametric Excitations," Complexity, Hindawi, vol. 2019, pages 1-20, December.
    4. Liu, Jian & Qiao, Zijian & Ding, Xiaojian & Hu, Bing & Zang, Chuanlai, 2021. "Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Gong, Xulu & Xu, Pengfei & Liu, Di & Zhou, Biliu, 2023. "Stochastic resonance of multi-stable energy harvesting system with high-order stiffness from rotational environment," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Gao, Fengyin & Kang, Yanmei, 2021. "Positive role of fractional Gaussian noise in FitzHugh–Nagumo neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Xu, Pengfei & Gong, Xulu & Wang, Haotian & Li, Yiwei & Liu, Di, 2023. "A study of stochastic resonance in tri-stable generalized Langevin system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    8. 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).

    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. Jin, Yanfei & Wang, Heqiang, 2020. "Noise-induced dynamics in a Josephson junction driven by trichotomous noises," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Bi, Haohao & Lei, Youming & Han, Yanyan, 2019. "Stochastic resonance across bifurcations in an asymmetric system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1296-1312.
    3. Margielewicz, Jerzy & Gąska, Damian & Litak, Grzegorz & Wolszczak, Piotr & Yurchenko, Daniil, 2022. "Nonlinear dynamics of a new energy harvesting system with quasi-zero stiffness," Applied Energy, Elsevier, vol. 307(C).
    4. Dongmei Huang & Shengxi Zhou & Zhichun Yang, 2019. "Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow-Band Stochastic Parametric Excitations," Complexity, Hindawi, vol. 2019, pages 1-20, December.
    5. Chen, Lin & Liao, Xin & Sun, Beibei & Zhang, Ning & Wu, Jianwei, 2022. "A numerical-experimental dynamic analysis of high-efficiency and broadband bistable energy harvester with self-decreasing potential barrier effect," Applied Energy, Elsevier, vol. 317(C).
    6. Rasel, Mohammad Sala Uddin & Park, Jae-Yeong, 2017. "A sandpaper assisted micro-structured polydimethylsiloxane fabrication for human skin based triboelectric energy harvesting application," Applied Energy, Elsevier, vol. 206(C), pages 150-158.
    7. Huguet, Thomas & Badel, Adrien & Druet, Olivier & Lallart, Mickaël, 2018. "Drastic bandwidth enhancement of bistable energy harvesters: Study of subharmonic behaviors and their stability robustness," Applied Energy, Elsevier, vol. 226(C), pages 607-617.
    8. Yildirim, Tanju & Ghayesh, Mergen H. & Li, Weihua & Alici, Gursel, 2017. "A review on performance enhancement techniques for ambient vibration energy harvesters," Renewable and Sustainable Energy Reviews, Elsevier, vol. 71(C), pages 435-449.
    9. Zhang, L.B. & Dai, H.L. & Abdelkefi, A. & Wang, L., 2019. "Experimental investigation of aerodynamic energy harvester with different interference cylinder cross-sections," Energy, Elsevier, vol. 167(C), pages 970-981.
    10. Xu, Pengfei & Gong, Xulu & Wang, Haotian & Li, Yiwei & Liu, Di, 2023. "A study of stochastic resonance in tri-stable generalized Langevin system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    11. Erkaymaz, Okan & Ozer, Mahmut, 2016. "Impact of small-world network topology on the conventional artificial neural network for the diagnosis of diabetes," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 178-185.
    12. Xiaobiao Shan & Haigang Tian & Han Cao & Tao Xie, 2020. "Enhancing Performance of a Piezoelectric Energy Harvester System for Concurrent Flutter and Vortex-Induced Vibration," Energies, MDPI, vol. 13(12), pages 1-19, June.
    13. Zhaoxin Cai & Kuntao Zhou & Tao Yang & Shuying Hao, 2023. "Analysis of Dynamic Characteristics of Tristable Exponential Section of Piezoelectric Energy Harvester," Energies, MDPI, vol. 16(18), pages 1-21, September.
    14. Wang, Zhemin & Du, Yu & Li, Tianrun & Yan, Zhimiao & Tan, Ting, 2021. "A flute-inspired broadband piezoelectric vibration energy harvesting device with mechanical intelligent design," Applied Energy, Elsevier, vol. 303(C).
    15. Qin, Jian & Zhang, Zhenquan & Huang, Shuting & Wang, Wei & Liu, Yanjun & Xue, Gang, 2024. "Energy capture performance enhancement of point absorber wave energy converter using magnetic tristable and quadstable mechanisms," Renewable Energy, Elsevier, vol. 221(C).
    16. Yu, Haitao & Guo, Xinmeng & Wang, Jiang & Deng, Bin & Wei, Xile, 2015. "Spike coherence and synchronization on Newman–Watts small-world neuronal networks modulated by spike-timing-dependent plasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 307-317.
    17. Zou, Donglin & Liu, Gaoyu & Rao, Zhushi & Tan, Ting & Zhang, Wenming & Liao, Wei-Hsin, 2021. "Design of a multi-stable piezoelectric energy harvester with programmable equilibrium point configurations," Applied Energy, Elsevier, vol. 302(C).
    18. Lee, Hyeon & Sharpes, Nathan & Abdelmoula, Hichem & Abdelkefi, Abdessattar & Priya, Shashank, 2018. "Higher power generation from torsion-dominant mode in a zigzag shaped two-dimensional energy harvester," Applied Energy, Elsevier, vol. 216(C), pages 494-503.
    19. Li, Wei & Zhang, Ying & Huang, Dongmei & Rajic, Vesna, 2022. "Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    20. Ge, Mengyan & Jia, Ya & Xu, Ying & Lu, Lulu & Wang, Huiwen & Zhao, Yunjie, 2019. "Wave propagation and synchronization induced by chemical autapse in chain Hindmarsh–Rose neural network," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 136-145.

    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:apmaco:v:346:y:2019:i:c:p:352-362. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.