THERMAL SCIENCE

International Scientific Journal

Yajie Li

,

Zhiqiang Wu

,

Yongtao Sun

,

Ying Hao

,

Xiangyun Zhang

,

Feng Wang

,

Heping Shi

ANALYSIS OF THE STATIONARY PROBABILITY DENSITY OF A GENERALIZED AND BISTABLE VAN DER POL SYSTEM EXCITED BY COLORED NOISE

ABSTRACT
The stochastic P-bifurcation behavior of bi-stability in a generalized van der Pol oscillator with the fractional damping under colored noise and thermal excitation is investigated. Firstly, using the principle of minimal mean square error and lin-earization method, 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 stationary probability density function is obtained by the stochastic averaging, and then based on the singularity theory, the critical parametric con-ditions for the system amplitude stochastic P-bifurcation are found. Finally, the types of the stationary probability density function of the system amplitude are qualitatively analyzed in each area divided by the transition set curves. The con-sistency between the analytical results and the numerical results acquired from Monte-Carlo simulation also testifies 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, Gaussian colored noise, fractional damping, critical parametric conditions, Monte-Carlo simulation
PAPER SUBMITTED: 2022-10-01
PAPER REVISED: 2023-03-01
PAPER ACCEPTED: 2023-05-22
PUBLISHED ONLINE: 2024-05-18
DOI REFERENCE: https://doi.org/10.2298/TSCI2403189L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE Issue 3, PAGES [2189 - 2199]
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Analysis of the stationary probability density of a generalized and bistable van der Pol system excited by colored noise

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence