THERMAL SCIENCE

International Scientific Journal

Yajie Li

,

Zhiqiang Wu

,

Qixun Lan

,

Yujie Cai

,

Huafeng Xu

,

Yongtao Sun

STOCHASTIC TRANSITION BEHAVIORS IN A TRI-STABLE VAN DER POL OSCILLATOR WITH FRACTIONAL DELAYED ELEMENT SUBJECT TO GAUSSIAN WHITE NOISE

ABSTRACT
The stochastic P-bifurcation behavior of tri stability in a generalized Van der Pol system with fractional derivative under additive Gaussian white noise excitation is investigated. Firstly, based on the minimal mean square error principle, the fractional derivative is found to be equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the stationary probability density function of the system amplitude is obtained by stochastic averaging, and according to the singularity theory, the critical parameters for stochastic P-bifurcation of the system are found. Finally, the nature of stationary probability density function curves of the system amplitude is qualitatively analyzed by choosing the corresponding parameters in each region divided by the transition set curves. The consistency between the analytical solutions and Monte-Carlo simulation results verifies the theoretical results in this paper.
KEYWORDS
stochastic P-bifurcation, fractional derivative, gaussian white noises, transition set curves, Monte-Carlo simulation
PAPER SUBMITTED: 2020-03-08
PAPER REVISED: 2021-10-01
PAPER ACCEPTED: 2021-10-01
PUBLISHED ONLINE: 2022-07-16
DOI REFERENCE: https://doi.org/10.2298/TSCI2203713L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 3, PAGES [2713 - 2725]
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Stochastic transition behaviors in a tri-stable van der Pol oscillator with fractional delayed element subject to Gaussian white noise

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