THERMAL SCIENCE

International Scientific Journal

Yajie Li

,

Yongtao Sun

,

Ying Hao

,

Xiangyun Zhang

,

Feng Wang

,

Heping Shi

,

Bin Wang

STOCHASTIC STABILITY OF THE FRACTIONAL AND TRI-STABLE VAN DER VOL OSCILLATOR WITH TIME-DELAY FEEDBACK DRIVEN BY GAUSSIAN WHITE NOISE

ABSTRACT
The stochastic P-bifurcation behavior of tri-stability in a fractional-order van der Pol system with time-delay feedback under additive Gaussian white noise excitation is investigated. Firstly, according to the equivalent principle, the fractional derivative and the time-delay term can be equivalent to a linear combination of damping and restoring forces, so the original system can be simplified into an equivalent integer-order system. Secondly, the stationary probability density function of the system amplitude is obtained by the stochastic averaging, and based on the singularity theory, the critical parameters for stochastic P-bifurcation of the system are found. Finally, the properties of stationary probability density function curves of the system amplitude are qualitatively analyzed by choosing corresponding parameters in each sub-region divided by the transition set curves. The consistence between numerical results obtained by Monte-Carlo simulation and analytical solutions has verified the accuracy of the theoretical analysis. The method used in this paper has a direct guidance in the design of fractional-order controller to adjust the dynamic behavior of the system.
KEYWORDS
stochastic P-bifurcation, fractional derivative, gaussian white noises, transition set curves, Monte-Carlo simulation
PAPER SUBMITTED: 2022-03-01
PAPER REVISED: 2022-07-24
PAPER ACCEPTED: 2022-07-24
PUBLISHED ONLINE: 2023-06-11
DOI REFERENCE: https://doi.org/10.2298/TSCI2303155L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 3, PAGES [2155 - 2164]
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Stochastic stability of the fractional and tri-stable Van der vol oscillator with time-delay feedback driven by Gaussian white noise

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