IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v201y2025ip1s0960077925014365.html

Stochastic bifurcations and chaos suppression in a quasi-zero stiffness isolator with time-delayed feedback control

Author

Listed:
  • Zhang, Ruocong
  • Han, Zikun
  • Wang, Qiubao

Abstract

This paper investigates stochastic bifurcation and chaos suppression in a quasi-zero stiffness (QZS) isolator under time-delayed feedback and combined random–harmonic excitation. First, it shows how varying the damping ratio triggers a Hopf bifurcation and that noise shrinks the stability region. Next, center manifold reduction and stochastic averaging reduce the system to a one-dimensional Itoˆ equation, whose stochastic bifurcation conditions are derived via singularity theory. To avoid misidentifying peaks in probability densities, topological data analysis (TDA) is used to detect bifurcations through persistent homology of superlevel sets. Results demonstrate that time-delayed feedback raises the chaos threshold and that confining the response to a unimodal distribution enhances stability. Finally, a “rapid optimization algorithm” scans parameter spaces to minimize the standard deviation transmissibility (SDT) while guaranteeing dynamical stability. Integrating nonlinear dynamics, delayed feedback, and TDA, the study offers a paradigm for designing high-performance QZS isolators in complex environments.

Suggested Citation

  • Zhang, Ruocong & Han, Zikun & Wang, Qiubao, 2025. "Stochastic bifurcations and chaos suppression in a quasi-zero stiffness isolator with time-delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925014365
    DOI: 10.1016/j.chaos.2025.117423
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925014365
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.117423?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. Chen, Xiyuan & Wang, Qiubao, 2024. "A novel dimensionality reduction approach by integrating dynamics theory and machine learning," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 98-111.
    2. Machado, M.R. & Dutkiewicz, M. & Colherinhas, G.B., 2024. "Metamaterial-based vibration control for offshore wind turbines operating under multiple hazard excitation forces," Renewable Energy, Elsevier, vol. 223(C).
    3. Wang, Yufei & Xing, Ying & Li, Xiaodi, 2025. "Stability of delayed switched systems involving impulses: State-dependent switching control approach," Chaos, Solitons & Fractals, Elsevier, vol. 194(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. Jacek Lukasz Wilk-Jakubowski & Lukasz Pawlik & Grzegorz Wilk-Jakubowski & Radoslaw Harabin, 2025. "State-of-the-Art in the Use of Renewable Energy Sources on the Example of Wind, Wave Energy, Tidal Energy, and Energy Harvesting: A Review from 2015 to 2024," Energies, MDPI, vol. 18(6), pages 1-26, March.
    2. Xu, Lianbing & Zhang, Gang & Huang, Xiaoxiao & He, Lin, 2025. "Adaptive stochastic resonance in an improved Izhikevich neuron model driven by multiplicative and additive Gaussian noise and its application in fault diagnosis of wind turbines," Renewable Energy, Elsevier, vol. 253(C).
    3. Yanfeng Wang & Chenghao Xu & Mengze Yu & Zhicong Huang, 2024. "Lightweight Design of Vibration Control Devices for Offshore Substations Based on Inerters," Sustainability, MDPI, vol. 16(8), pages 1-21, April.
    4. Li, Lili & Li, Mengjie & Gao, Lijun & Li, Yecheng, 2026. "Tri-sequential Stackelberg game with defensive switching against deception attacks for networked switched systems," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).

    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:201:y:2025:i:p1:s0960077925014365. 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.