中国物理B ›› 2015, Vol. 24 ›› Issue (6): 60504-060504.doi: 10.1088/1674-1056/24/6/060504

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A circular zone counting method of identifying a Duffing oscillator state transition and determining the critical value in weak signal detection

李梦平, 许雪梅, 杨兵初, 丁家峰   

  1. School of Physics and Electronics, Central South University, Changsha 410083, China
  • 收稿日期:2014-11-23 修回日期:2015-01-13 出版日期:2015-06-05 发布日期:2015-06-05
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61172047 and 61071025).

A circular zone counting method of identifying a Duffing oscillator state transition and determining the critical value in weak signal detection

Li Meng-Ping (李梦平), Xu Xue-Mei (许雪梅), Yang Bing-Chu (杨兵初), Ding Jia-Feng (丁家峰)   

  1. School of Physics and Electronics, Central South University, Changsha 410083, China
  • Received:2014-11-23 Revised:2015-01-13 Online:2015-06-05 Published:2015-06-05
  • Contact: Xu Xue-Mei E-mail:xuxuemei999@126.com
  • About author:05.45.-a
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61172047 and 61071025).

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摘要： Identifying state transition and determining the critical value of the Duffing oscillator are crucial to indicating external signal existence and have a great influence on detection accuracy in weak signal detection. A circular zone counting (CZC) method is proposed in this paper, by combining the Duffing oscillator's phase trajectory feature and numerical calculation for quickly and accurately identifying state transition and determining the critical value, to realize a high-efficiency weak signal detection. Detailed model analysis and method construction of the CZC method are introduced. Numerical experiments into the reliability of the proposed CZC method compared with the maximum Lyapunov exponent (MLE) method are carried out. The CZC method is demonstrated to have better detecting ability than the MLE method, and furthermore it is simpler and clearer in calculation to extend to engineering application.

关键词: identifying state transition, determining critical value, Duffing oscillator, circular zone counting method, maximum Lyapunov exponent method

Abstract: Identifying state transition and determining the critical value of the Duffing oscillator are crucial to indicating external signal existence and have a great influence on detection accuracy in weak signal detection. A circular zone counting (CZC) method is proposed in this paper, by combining the Duffing oscillator's phase trajectory feature and numerical calculation for quickly and accurately identifying state transition and determining the critical value, to realize a high-efficiency weak signal detection. Detailed model analysis and method construction of the CZC method are introduced. Numerical experiments into the reliability of the proposed CZC method compared with the maximum Lyapunov exponent (MLE) method are carried out. The CZC method is demonstrated to have better detecting ability than the MLE method, and furthermore it is simpler and clearer in calculation to extend to engineering application.

Key words: identifying state transition, determining critical value, Duffing oscillator, circular zone counting method, maximum Lyapunov exponent method

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a