Physical mechanism of the chaotic detection of the unknown frequency of weak harmonic signal and effects of damping ratio on the detection results
Li Yue (李月)a, Yang Bao-Jun (杨宝俊)b, Deng Xiao-Ying (邓小英)a, Jin Lei (金雷)a, Du Li-Zhi (杜立志)a
a Department of Information Engineering, Jilin University, Changchun 130012, China; b Department of Geophysics, Jilin University, Changchun 130026, China
Abstract In the zero-order approximation, we use the perturbation method of parameter with small magnitude to prove that the harmonic frequency in the solution of the equation is close to that of the driving force when the chaotic system from Duffing－Holmes equation stays in the stable periodic state, which is the physical mechanism of the detection of the unknown frequency of weak harmonic signal using the chaotic theory. The result of the simulation experiment shows that the method proposed in this paper, by which one can determine the frequency of the stable system from the number of circulation change of the phase state directionally across a fixed phase state point ($x,\dot{x}$) in fixed simulation time period, is successful. Analyzing the effects of the damping ratio on the chaotic detection result, one can see that for different frequency ranges it is necessary to carefully choose corresponding damping ratio $\alpha$.
Received: 14 January 2004
Revised: 10 May 2004
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 40374045).
Cite this article:
Li Yue (李月), Yang Bao-Jun (杨宝俊), Deng Xiao-Ying (邓小英), Jin Lei (金雷), Du Li-Zhi (杜立志) Physical mechanism of the chaotic detection of the unknown frequency of weak harmonic signal and effects of damping ratio on the detection results 2004 Chinese Physics 13 1386
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