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Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative
Joint Authors
Yang, Shaopu
Shen, Yongjun
Wei, Peng
Sui, Chuanyi
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-02-25
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
The subharmonic resonance of van der Pol (VDP) oscillator with fractional-order derivative is studied by the averaging method.
At first, the first-order approximate solutions are obtained by the averaging method.
Then the definitions of equivalent linear damping coefficient (ELDC) and equivalent linear stiffness coefficient (ELSC) for subharmonic resonance are established, and the effects of the fractional-order parameters on the ELDC, the ELSC, and the dynamical characteristics of system are also analysed.
Moreover, the amplitude-frequency equation and phase-frequency equation of steady-state solution for subharmonic resonance are established.
The corresponding stability condition is presented based on Lyapunov theory, and the existence condition for subharmonic resonance (ECSR) is also obtained.
At last, the comparisons of the fractional-order and the traditional integer-order VDP oscillator are fulfilled by the numerical simulation.
The effects of the parameters in fractional-order derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied.
American Psychological Association (APA)
Shen, Yongjun& Wei, Peng& Sui, Chuanyi& Yang, Shaopu. 2014. Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-17.
https://search.emarefa.net/detail/BIM-494725
Modern Language Association (MLA)
Shen, Yongjun…[et al.]. Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative. Mathematical Problems in Engineering No. 2014 (2014), pp.1-17.
https://search.emarefa.net/detail/BIM-494725
American Medical Association (AMA)
Shen, Yongjun& Wei, Peng& Sui, Chuanyi& Yang, Shaopu. Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-17.
https://search.emarefa.net/detail/BIM-494725
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-494725