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Possibilities of the Discrete Fourier Transform for Determining the Order-Chaos Transition in a Dynamical System

Carlos R. Fadragas·Juan V. Lorenzo-Ginori·Ruben Orozco-Morales
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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 $x[n+1]=rx[n](1-x[n])$. 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.

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BibTeXRIS

Carlos R. Fadragas, Juan V. Lorenzo-Ginori, Ruben Orozco-Morales. 2002-03-07. Possibilities of the Discrete Fourier Transform for Determining the Order-Chaos Transition in a Dynamical System. https://arxiv.org/abs/nlin/0203010

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