| Issue |
Wuhan Univ. J. Nat. Sci.
Volume 28, Number 5, October 2023
|
|
|---|---|---|
| Page(s) | 421 - 432 | |
| DOI | https://doi.org/10.1051/wujns/2023285421 | |
| Published online | 10 November 2023 | |
Mathematics
CLC number: O324
Response and Bifurcation of Fractional Duffing Oscillator under Combined Recycling Noise and Time-Delayed Feedback Control
School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
† To whom correspondence should be addressed. E-mail: Zhangjg7715776@126.com
Received:
26
March
2023
Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiffness term, the fractional derivative is equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the Itô differential equations and one-dimensional Markov process are obtained according to stochastic averaging method, and the stochastic stability and stochastic bifurcation of the system are analyzed. Lastly, through joint probability density function diagram and the stationary probability density function diagram, the stochastic bifurcation behavior of system under the different time-delay, fractional order and noise intensity are discussed respectively, the validity of the theory and the occurrence of bifurcation phenomenon are verified.
Key words: recycling noise / time-delay / fractional derivative / stochastic averaging method / stochastic bifurcation
Biography: WANG Fang, female, research direction: applied mathematics. E-mail: 194114327@qq.com
Fundation item: Supported by the National Natural Science Foundation of China (61863022) and the Key Project of Gansu Province Natural Science Foundation (23JRRA882)
© Wuhan University 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.