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ORIGINAL RESEARCH article
Front. Phys.
Sec. Interdisciplinary Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1567842
This article is part of the Research TopicNonlinear Vibration and Instability in Nano/Micro Devices: Principles and Control StrategiesView all 16 articles
Stochastic bifurcation phenomenon and multi-stable behaviors of a fractional Rayleigh-Duffing oscillator under recycling noise
Provisionally accepted- 1Henan University of Urban Construction, Pingdingshan, China
- 2Tianjin University, Tianjin, Tianjin, China
- 3Tianjin Sino-German University of Applied Sciences, Tianjin, China
- 4East China Jiaotong University, Nanchang, Jiangxi, China
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This study examines the stochastic bifurcation phenomenon in a fractional and multistable Rayleigh-Duffing oscillator subjected to recycling noise excitation. First, using the harmonic balance method and minimizing the mean-square error, an approximate integer-order equivalent system is derived for the original fractional-order system. Subsequently, the steady-state probability density function (sPDF) of the system amplitude is obtained via stochastic averaging. The critical conditions for stochastic P-bifurcation (SPB) are then determined using singularity theory. The stationary PDF curves of the system amplitude are qualitatively analyzed across regions delineated by transition set curves. Finally, Monte Carlo simulations confirm the analytical findings, validating the theoretical framework. These results provide insights for improving system response control through fractionalorder controller design.
Keywords: stochastic P-bifurcation1, fractional damping2, stochastic averaging method3, transition set curves4, Monte Carlo simulation5
Received: 28 Jan 2025; Accepted: 19 Mar 2025.
Copyright: © 2025 Li, Wu, Sun, Zhang and Chen. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Zhi-Qiang Wu, Tianjin University, Tianjin, 300072, Tianjin, China
Yong-Tao Sun, Tianjin University, Tianjin, 300072, Tianjin, China
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