STOCHASTIC STABILITY AND PARAMETRIC CONTROL IN A GENERALIZED AND TRI-STABLE VAN DER POL SYSTEM WITH FRACTIONAL ELEMENT DRIVEN BY MULTIPLICATIVE NOISE

Ya-Jie Li, Zhi-Qiang Wu (), Yong-Tao Sun (), Ying Hao, Xiang-Yun Zhang, Feng Wang and He-Ping Shi
Additional contact information
Ya-Jie Li: Henan Engineering Research Centre of Building-Photovoltaics, School of Mathematics and Physics, Henan University of Urban, Construction, Pingdingshan, P. R. China
Zhi-Qiang Wu: ��Tianjin Key Laboratory of Nonlinear Dynamics and Control, School of Mechanical Engineering, Tianjin, University, Tianjin, P. R. China
Yong-Tao Sun: ��Tianjin Key Laboratory of Nonlinear Dynamics and Control, School of Mechanical Engineering, Tianjin, University, Tianjin, P. R. China
Ying Hao: ��School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, P. R. China
Xiang-Yun Zhang: �Basic Course Department, Tianjin Sino-German, University of Applied Sciences, Tianjin, P. R. China
Feng Wang: �School of Automobile and Transportation, Tianjin University of Technology and Education, Tianjin, P. R. China
He-Ping Shi: �School of Automobile and Transportation, Tianjin University of Technology and Education, Tianjin, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 07, 1-13

Abstract: The stochastic transition behavior of tri-stable states in a fractional-order generalized Van der Pol (VDP) system under multiplicative Gaussian white noise (GWN) excitation is investigated. First, according to the minimal mean square error (MMSE) concept, the fractional derivative can be equivalent to a linear combination of damping and restoring forces, and the original system can be simplified into an equivalent integer-order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and based on singularity theory, the critical parameters for stochastic P-bifurcation of the system are found. Finally, the properties of stationary PDF curves of the system amplitude are qualitatively analyzed by choosing the corresponding parameters in each sub-region divided by the transition set curves. The consistency between numerical results obtained by Monte-Carlo simulation and analytical solutions verified the accuracy of the theoretical analysis process and the method used in this paper has a direct guidance in the design of fractional-order controller to adjust the system behavior.

Keywords: Stochastic P-Bifurcation; Fractional Derivative; Multiplicative Gaussian White Noises; Transition Set Curves; Monte-Carlo Simulation (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X23500834
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:31:y:2023:i:07:n:s0218348x23500834

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X23500834

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().