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. (Astron Astrophys 359(1):386–396, 2000), we propose a new tool, namely the power spectrum indicator (PSI), \(\psi ^2\) , that enables us to determine, as early as possible, whether an orbit of an n-dimensional map is chaotic or not. In the present work, we have tested the method in 2-D and 4-D maps. This new method is based on the frequency analysis of a data series constructed by recording the logarithm of the amplification factor of the deviation vector of nearby orbits. Accordingly, two datasets are recorded and the \(\chi ^2\) -likelihood 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 nonzero \(\psi ^2\) 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.
