THERMAL SCIENCE

International Scientific Journal

Yajie Li

,

Zhiqiang Wu

,

Qixun Lan

,

Yujie Cai

,

Huafeng Xu

,

Yongtao Sun

STOCHASTIC TRANSITION BEHAVIORS IN A GENERALIZED VAN DER POL OSCILLATOR WITH FRACTIONAL DAMPING UNDER GAUSSIAN WHITE NOISE

ABSTRACT
The stochastic P-bifurcation behavior of bi-stability in a generalized Van der Pol oscillator with a fractional damping under multiplicative Gaussian white noise excitation is investigated. Firstly, using the principle of minimal mean square error, the non-linear stiffness terms can be equivalent to a linear stiffness which is a function of the system amplitude, and the original system is simplified to an equivalent integer order Van der Pol system. Secondly, the system amplitude’s stationary probability density function is obtained by stochastic averaging. Then according to the singularity theory, the critical parametric conditions for the sys-tem amplitude’s stochastic P-bifurcation are found. Finally, the types of the system’s stationary probability density function curves of amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical results and the numerical results obtained from Monte-Carlo simulation verifies the theoretical analysis in this paper and the method used in this paper can directly guide the design of the fractional order controller to adjust the response of the system.
KEYWORDS
stochastic P-bifurcation, fractional damping, Gaussian white noise, transition set, Monte Carlo simulation
PAPER SUBMITTED: 2019-12-01
PAPER REVISED: 2020-06-01
PAPER ACCEPTED: 2020-06-01
PUBLISHED ONLINE: 2021-03-27
DOI REFERENCE: https://doi.org/10.2298/TSCI191201125L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 3, PAGES [2347 - 2356]
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Stochastic transition behaviors in a generalized Van der Pol oscillator with fractional damping under Gaussian white noise

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