Possibilities of the Discrete Fourier Transform for Determining the Order-Chaos Transition in a Dynamical System
Abstract
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples equally spaced in the frequency domain. The Fast Fourier Transform (FFT) algoritm allows us an effective computation, and it can be applied to a relatively short time series. DFT representation requirements were analized and applied for determining the order-chaos transition in a nonlinear system described by the equation . Its effectiveness was demonstrated by comparing the results with those obtained by calculating the largest Lyapounov exponent for the time series set, obtained from the logistic equation.
Keywords
Cite
@article{arxiv.nlin/0203010,
title = {Possibilities of the Discrete Fourier Transform for Determining the Order-Chaos Transition in a Dynamical System},
author = {Carlos R. Fadragas and Juan V. Lorenzo-Ginori and Ruben Orozco-Morales},
journal= {arXiv preprint arXiv:nlin/0203010},
year = {2007}
}
Comments
14pages, 6figures