This study aims to investigate the harmonic resonance of third-order forced van der Pol oscillator with fractional-order derivative using the asymptotic method. The approximately analytical solution for the system is first determined, and the amplitude–frequency equation of the oscillator is established. The stability condition of the harmonic solution is then obtained by means of Lyapunov theory. A comparison between the traditional integer-order of forced van der Pol oscillator and the considered fractional-order one follows the numerical simulation. Finally, the numerical results are analyzed to show the influences of the parameters in the fractional-order derivative on the steady-state amplitude, the amplitude–frequency curves, and the system stability.
Resonance Oscillation of Third-Order Forced van der Pol System With Fractional-Order Derivative
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 13, 2015; final manuscript received April 27, 2016; published online May 24, 2016. Assoc. Editor: Dumitru Baleanu.
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Van Khang, N., Thuy, B. T., and Chien, T. Q. (May 24, 2016). "Resonance Oscillation of Third-Order Forced van der Pol System With Fractional-Order Derivative." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 041030. https://doi.org/10.1115/1.4033555
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