Frequency analysis with coupled nonlinear oscillators

被引:45
作者
Buchli, Jonas [1 ]
Righetti, Ludovic [1 ]
Ijspeert, Auke Jan [1 ]
机构
[1] Ecole Polytech Fed Lausanne, Sch Comp & Commun Sci, Stn 14, CH-1015 Lausanne, Switzerland
关键词
frequency analysis; coupled oscillators; adaptive frequency oscillator;
D O I
10.1016/j.physd.2008.01.014
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a method to obtain the frequency spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive frequency oscillators with negative mean-field coupling. For the frequency analysis, the synchronization and adaptation properties of the component oscillators are exploited. The frequency spectrum of the signal is reflected in the statistics of the intrinsic frequencies of the oscillators. The frequency analysis is completely embedded in the dynamics of the system. Thus, no pre-processing or additional parameters, such as time windows, are needed. Representative results of the numerical integration of the system are presented. It is shown, that the oscillators tune to the correct frequencies for both discrete and continuous spectra. Due to its dynamic nature the system is also capable to track non-stationary spectra. Further, we show that the system can be modeled in a probabilistic manner by means of a nonlinear Fokker-Planck equation. The probabilistic treatment is in good agreement with the numerical results, and provides a useful tool to understand the underlying mechanisms leading to convergence. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码:1705 / 1718
页数:14
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