关键词: 基频变换, 不可预测性, 回归频度, 周期轨道, 混沌

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