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

Ruocong Zhang, Zikun Han and Qiubao Wang

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

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.

Keywords: Quasi-zero stiffness; Stochastic bifurcation; Time-delay; Vibration isolation (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925014365
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925014365

DOI: 10.1016/j.chaos.2025.117423

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().