Spectral analysis of the Lorenz attractor

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Spectral analysis of the Lorenz attractor

H. Ali Pacha, W. Aggoune, S. Hamaci, P. Lorenz, A. Ali Pacha

Article ID: 2911
Vol 3, Issue 1, 2025

DOI: https://doi.org/10.54517/cte2911

Received: 30 August 2024; Accepted: 15 October 2024; Available online: 27 February 2025; Issue release: 31 March 2025

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Abstract

For a long time, chaos was considered uncontrollable and unusable. However, over the past thirty years, researchers have formulated equations for certain chaotic phenomena, revealing a deterministic aspect to what initially seems random. The evolution of chaotic systems is characterized by strange attractors, which, despite their complex nature, do not allow precise long-term predictions of system behavior. The Lorenz attractor is the best-known example and was the first to be studied, though many other attractors with unusual shapes have since been discovered. The aim of this work is to perform a spectral analysis of the Lorenz attractor by examining the frequencies present in the time signals generated by the solutions of the Lorenz system of equations. To evaluate the frequency complexity of these signals, the discrete Fast Fourier Transform (FFT) is used to derive their frequency spectrum.

Keywords

fast Fourier transform; spectral analysis; strange attractor; Lorenz attractor

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