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

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

中国物理B ›› 2018, Vol. 27 ›› Issue (12): 120502-120502.doi: 10.1088/1674-1056/27/12/120502

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

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

Sujuan Li(李素娟), Jiangchuan Niu(牛江川), Xianghong Li(李向红)

1 School of Information Science and Technology, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
2 School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
3 Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

收稿日期:2018-08-24 修回日期:2018-09-29 出版日期:2018-12-05 发布日期:2018-12-05
通讯作者: Jiangchuan Niu E-mail:menjc@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11872254 and 11672191).

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

Sujuan Li(李素娟)¹, Jiangchuan Niu(牛江川)², Xianghong Li(李向红)³

1 School of Information Science and Technology, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
2 School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
3 Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

Received:2018-08-24 Revised:2018-09-29 Online:2018-12-05 Published:2018-12-05
Contact: Jiangchuan Niu E-mail:menjc@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11872254 and 11672191).

摘要/Abstract

摘要：

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.

关键词: fractional-order oscillator, harmonic balance method, primary resonance

Abstract:

Key words: fractional-order oscillator, harmonic balance method, primary resonance

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

45.10.Hj (Perturbation and fractional calculus methods)

李素娟, 牛江川, 李向红. Primary resonance of fractional-order Duffing-van der Pol oscillator by harmonic balance method[J]. 中国物理B, 2018, 27(12): 120502-120502.

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[J]. Chin. Phys. B, 2018, 27(12): 120502-120502.

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

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

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