Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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A Study on the Nonlinearity of Chaotic Signal by Bispectral Analysis

바이스펙트럼 해석에 의한 카오스 신호의 비선형성에 관한 연구

  • Published : 2007.08.01
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Abstract

During thirty years, deterministic chaos has moved center stage in many areas of applied mathematics. One important stimulus for this, particularly in the early 1970s, was work on nonlinear aspects of the dynamics of plant and animal populations. There are many situations, at least to a crude first approximation, by a simple first-order difference equation. Past studies have shown that such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behavior, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. But higher-order spectral analyses of such behavior are usually not considered. Higher-order spectra of a signal contain important information that is not present in its power spectrum. So, if we find the spectral pattern and get information from it, it will be able to be used effectively in so many fields. Hence, this paper uses auto bicoherence and bicoherence residue which are sort of bispectrum. Applying these to behavior of logistic difference equation, which is typical chaotic signal, the phenomenon of phase coupling and the appearance of frequency band can be analyzed. Such information means that bispectral analysis is useful to detect nonlinearity of signal.

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References

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