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- W2885894410 abstract "To determine the regular or chaotic nature of the orbits in dynamical systems can be quite an issue. In this article, following Vozikis et al. (2000), we propose a new tool, namely, the Power Spectrum Indicator (PSI), $psi^2$, that enables us to determine, as early as posible, whether an orbit of a two-dimensional map is chaotic or not. This new method is based on the frequency analysis of a data series constucted by recording the logarithm of the amplification factor of the deviation vector of nearby orbits. Accordingly, two datasets are recorded and the $chi^2$-likelyhood of their power spectra is computed. Ordered orbits have always the same power spectrum, so their $chi^2 equiv psi^2$ acquires a zero value. On the contrary, a chaotic orbit has a power spectrum that varies with time, hence, chaotic orbits always exhibit a non-zero $psi^2$ value. Even as regards sticky orbits, the PSI method is very effective in the early detection of chaos, while the global behavior of the $psi^2$ indicator can provide information (also) on the intense of the chaotic behavior, i.e., on how strong or weak the associated chaos may be." @default.
- W2885894410 created "2018-08-22" @default.
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- W2885894410 date "2018-08-01" @default.
- W2885894410 modified "2023-09-27" @default.
- W2885894410 title "The power spectrum indicator: A new, efficient method for the early detection of chaos" @default.
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