中国物理B ›› 2009, Vol. 18 ›› Issue (3): 958-968.doi: 10.1088/1674-1056/18/3/020

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Regular nonlinear response of the driven Duffing oscillator to chaotic time series

Danilo P. Mandic1, 杨宝俊2, 袁野3, 李月3   

  1. (1)Department of Electrical and Electronic Engineering, Imperial College, London SW72BT, UK; (2)Department of Geophysics, Jilin University, Changchun 130026, China; (3)School of Communication Engineering, Jilin University, Changchun 130012, China
  • 收稿日期:2008-07-16 修回日期:2008-08-28 出版日期:2009-03-20 发布日期:2009-03-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 40574051 and 40774054).

Regular nonlinear response of the driven Duffing oscillator to chaotic time series

Yuan Ye(袁野)a), Li Yue(李月)a)†, Danilo P. Mandicb), and Yang Bao-Jun(杨宝俊)c)   

  1. a School of Communication Engineering, Jilin University, Changchun 130012, China; b Department of Electrical and Electronic Engineering, Imperial College, London SW72BT, UK; c Department of Geophysics, Jilin University, Changchun 130026, China
  • Received:2008-07-16 Revised:2008-08-28 Online:2009-03-20 Published:2009-03-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 40574051 and 40774054).

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摘要： Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated.

关键词: Duffing oscillator, chaotic time series, phase plane diagram, largest Lyapunov exponent

Abstract: Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated.

Key words: Duffing oscillator, chaotic time series, phase plane diagram, largest Lyapunov exponent

中图分类号:  (Time series analysis)

  • 05.45.Tp
05.45.Pq (Numerical simulations of chaotic systems)