2002/03/07 by Carlos R. Fadragas, Juan V. Lorenzo‐Ginori, Juan V. Lorenzo-Ginori +5
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0203010
14pages, 6figures
arxiv created 2002/03/07 · openalex publication_date 2002/03/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.