Journal of South China University of Technology (Natural Science Edition) ›› 2009, Vol. 37 ›› Issue (10): 5-10.

• Electronics, Communication & Automation Technology • Previous Articles     Next Articles

Fundamental Frequency Transformation and Unpredictability Estimation Algorithm of Chaotic Systems

Jin Jian-xiu  Qiu Shui-sheng  Liu Yun-liang   

  1. School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510640, Guangdong, China
  • Received:2008-10-16 Revised:2008-12-23 Online:2009-10-25 Published:2009-10-25
  • Contact: 晋建秀（1975-），女，博士生，主要从事混沌系统与保密通信研究． E-mail:jxjin@scut．edu．cn
  • About author:晋建秀（1975-），女，博士生，主要从事混沌系统与保密通信研究．
  • Supported by:

    国家自然科学基金资助项目（60372004）;广东省自然科学基金资助项目（06025729）

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Abstract:

In this paper, first, a method of fundamental frequency transformation for chaotic systems is proposed based on the concept of frequency domain analysis in the periodic orbit theory of chaotic attractors and on the matrix principle. Then, by using this method, Lorenz and Chua circuits are realized with different fundamental frequencies, and the corresponding frequency spectra are tested. Moreover, some experiments are carried out to verify the correctness of the proposed method, and an unpredictability estimation algorithm of chaotic systems is discussed. Finally, an improved formula for calculating the regression frequency is deduced. The proposed formula is also used to compare the unpredictability between Lorenz and Chua circuits with the same fundamental frequency of 3 kHz. The results indicate that the presented formula greatly improves the unpredictability estimation accuracy of different chaotic systems.

Key words: fundamental frequency transformation, unpredictability, regression frequency, periodic orbit, chaos