IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v199y2025ip3s0960077925008884.html

Unified signal response for stochastic resonance in bistable systems

Author

Listed:
  • Liu, Cong
  • Song, Xin-Ze
  • Wu, Zhi-Xi
  • Yuan, Guo-Yong

Abstract

Stochastic resonance, wherein the stimulus–response of a system can be maximally improved by an intermediate level of noise, has been extensively verified in coupled dynamical systems immersed in colored noisy environments. As yet the roles of noise color, coupling, damping, and the external driving frequency on the signal response remain largely unclear. Here, based on linear response theory, we comprehensively investigate the signal response of systems ranging from a single overdamped bistable oscillator perturbed by Gaussian white noise to the mean-field coupled underdamped Duffing elements disturbed by Ornstein–Uhlenbeck noise. We find that the signal response expressions in these different conditions can be summarized into a uniform Lorentz function form. Furthermore, based on the general formula, we explain explicitly the roles of driving frequency, coupling, and noise color on stochastic resonance. Since bistable systems have served as a testbed to utilize weak signals in energy harvesting devices and colloidal particles, our results thus have theoretical guidance significance on the manipulation of weak signals in realistic fields.

Suggested Citation

  • Liu, Cong & Song, Xin-Ze & Wu, Zhi-Xi & Yuan, Guo-Yong, 2025. "Unified signal response for stochastic resonance in bistable systems," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925008884
    DOI: 10.1016/j.chaos.2025.116875
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925008884
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116875?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. Li, Mengdi & Shi, Peiming & Zhang, Wenyue & Han, Dongying, 2021. "A novel underdamped continuous unsaturation bistable stochastic resonance method and its application," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Kang, Yan-Mei & Xie, Yong & Xu, Jian-Xue, 2006. "Observing nonlinear stochastic resonance with piecewise constant driving forces by the method of moments," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 715-721.
    3. Gao, Fengyin & Kang, Yanmei, 2021. "Positive role of fractional Gaussian noise in FitzHugh–Nagumo neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Robert L. Badzey & Pritiraj Mohanty, 2005. "Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance," Nature, Nature, vol. 437(7061), pages 995-998, October.
    5. 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).
    6. Guo, Yongfeng & Ding, Jiaxin & Mi, Lina, 2024. "Statistical complexity and stochastic resonance of an underdamped bistable periodic potential system excited by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    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. Yang, GuiJiang & Ai, Hao & Liu, Wei & Wang, Qiubao, 2023. "Weak signal detection based on variable-situation-potential with time-delay feedback and colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Ren, Yuhao & Pan, Yan & Duan, Fabing, 2022. "SNR gain enhancement in a generalized matched filter using artificial optimal noise," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Jiang, Jiahao & Li, Kaiyuan & Guo, Wei & Du, Luchun, 2021. "Energetic and entropic vibrational resonance," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Duan, Lingling & Ren, Yuhao & Duan, Fabing, 2022. "Adaptive stochastic resonance based convolutional neural network for image classification," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Qiao, Zijian & Shu, Xuedao, 2021. "Coupled neurons with multi-objective optimization benefit incipient fault identification of machinery," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. Huang, Xiaoxiao & Zhang, Gang & Xu, Jiaqi, 2025. "Adaptive multi-parameter constrained time-delay feedback tri-stable stochastic resonance combined with EEMD for rolling bearing fault diagnosis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 659(C).
    7. 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).
    8. Xu, Pengfei & Gong, Xulu & Zhang, Yanxia & Wang, Guotao, 2025. "Coherence of a periodic potential system with nonlinear nonlocal dissipation and colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    9. Kang, Yan-Mei & Jiang, Yao-Lin, 2009. "Observing bifurcation and resonance in a mean-field coupled periodically driven noisy overdamped oscillators by the method of moments," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1987-1993.
    10. Ai, Hao & Yang, GuiJiang & Liu, Wei & Wang, Qiubao, 2023. "A fast search method for optimal parameters of stochastic resonance based on stochastic bifurcation and its application in fault diagnosis of rolling bearings," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    11. Liu, Huixia & Lu, Lulu & Zhu, Yuan & Wei, Zhouchao & Yi, Ming, 2022. "Stochastic resonance: The response to envelope modulation signal for neural networks with different topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    12. He, Lifang & Xiong, Qing & Bi, Lujie, 2024. "Optimizing DSFH communication system performance via multi-feedback unsaturated tri-stable stochastic resonance for enhancement of periodic signal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 650(C).
    13. Wu, Yan & Wu, Liqing & Zhu, Yuan & Yi, Ming & Lu, Lulu, 2024. "Enhancing weak signal propagation by intra- and inter-layer global couplings in a feedforward network," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    14. Vocca, Helios & Neri, Igor & Travasso, Flavio & Gammaitoni, Luca, 2012. "Kinetic energy harvesting with bistable oscillators," Applied Energy, Elsevier, vol. 97(C), pages 771-776.
    15. Liao, Zhiqiang & Ma, Kaijie & Tang, Siyi & Sarker, Md Shamim & Yamahara, Hiroyasu & Tabata, Hitoshi, 2021. "Phase locking of ultra-low power consumption stochastic magnetic bits induced by colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    16. Ueda, Michihito, 2010. "Improvement of signal-to-noise ratio by stochastic resonance in sigmoid function threshold systems, demonstrated using a CMOS inverter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 1978-1985.
    17. Xie, Tianting & Ji, Yuandong & Yang, Zhongshan & Duan, Fabing & Abbott, Derek, 2023. "Optimal added noise for minimizing distortion in quantizer-array linear estimation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    18. Cheng, Guanghui & Liu, Weidan & Gui, Rong & Yao, Yuangen, 2020. "Sine-Wiener bounded noise-induced logical stochastic resonance in a two-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    19. Wei, Guoliang & Shu, Huisheng, 2007. "H∞ filtering on nonlinear stochastic systems with delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 663-670.
    20. Ma, Xindong & Zhang, Zhao, 2024. "Symmetric and asymmetric bursting oscillations in a hybrid van der Pol-Duffing-Rayleigh system," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).

    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:chsofr:v:199:y:2025:i:p3:s0960077925008884. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.