Primary Resonance of van der Pol Oscillator under Fractional-Order Delayed Feedback and Forced Excitation
Joint Authors
Chen, Jufeng
Li, Xianghong
Tang, Jianhua
Liu, Yafeng
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-12-18
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
The primary resonance of van der Pol oscillator under fractional-order delayed negative feedback and forced excitation is studied.
Firstly, the approximate analytical solution is obtained based on the averaging method, and it could be found that the fractional-order delayed feedback has not only the property of delayed velocity feedback but also that of delayed displacement feedback.
Moreover, the amplitude-frequency equation for the steady-state solution is established, and its stability conditions are also obtained.
Then, the results of the approximate analytical solution and numerical integration are compared and analyzed.
The agreement between the two methods is very high, so that the correctness and accuracy of the approximate analytical solution are verified.
Finally, the effects of all the parameters in the fractional-order delayed feedback on the amplitude-frequency curves are analyzed.
It could be concluded that fractional-order delayed feedback has important influences on the dynamical behavior of van der Pol oscillator, which is very significant to the optimization and control of a similar system.
American Psychological Association (APA)
Chen, Jufeng& Li, Xianghong& Tang, Jianhua& Liu, Yafeng. 2017. Primary Resonance of van der Pol Oscillator under Fractional-Order Delayed Feedback and Forced Excitation. Shock and Vibration،Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1204750
Modern Language Association (MLA)
Chen, Jufeng…[et al.]. Primary Resonance of van der Pol Oscillator under Fractional-Order Delayed Feedback and Forced Excitation. Shock and Vibration No. 2017 (2017), pp.1-9.
https://search.emarefa.net/detail/BIM-1204750
American Medical Association (AMA)
Chen, Jufeng& Li, Xianghong& Tang, Jianhua& Liu, Yafeng. Primary Resonance of van der Pol Oscillator under Fractional-Order Delayed Feedback and Forced Excitation. Shock and Vibration. 2017. Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1204750
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1204750