Primary resonance of fractional-order Duffing-van der Pol oscillator by harmonic balance method

doi:10.1088/1674-1056/27/12/120502

Abstract

The dynamical properties of fractional-order Duffing-van der Pol oscillator are studied, and the amplitude-frequency response equation of primary resonance is obtained by the harmonic balance method. The stability condition for steady-state solution is obtained based on Lyapunov theory. The comparison of the approximate analytical results with the numerical results is fulfilled, and the approximations obtained are in good agreement with the numerical solutions. The bifurcations of primary resonance for system parameters are analyzed. The results show that the harmonic balance method is effective and convenient for solving this problem, and it provides a reference for the dynamical analysis of similar nonlinear systems.

Keywords: fractional-order oscillator harmonic balance method primary resonance

Received: 24 August 2018
Revised: 29 September 2018
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	45.10.Hj	(Perturbation and fractional calculus methods)

Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11872254 and 11672191).

Corresponding Authors: Jiangchuan Niu
E-mail: menjc@163.com

Cite this article:

Sujuan Li(李素娟), Jiangchuan Niu(牛江川), Xianghong Li(李向红) Primary resonance of fractional-order Duffing-van der Pol oscillator by harmonic balance method 2018 Chin. Phys. B 27 120502

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Primary resonance of fractional-order Duffing-van der Pol oscillator by harmonic balance method

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