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

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dc.creatorFadragas, Carlos R.
dc.creatorLorenzo-Ginori, Juan V.
dc.creatorOrozco-Morales, Ruben
dc.date2002-03-07
dc.date.accessioned2026-07-07T05:33:57Z
dc.date.available2026-07-07T05:33:57Z
dc.descriptionThis 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.
dc.description14pages, 6figures
dc.identifierhttps://arxiv.org/abs/nlin/0203010
dc.identifierhttp://arxiv.org/abs/nlin/0203010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80187
dc.subjectChaotic Dynamics
dc.titlePossibilities of the Discrete Fourier Transform for Determining the Order-Chaos Transition in a Dynamical System
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