Applying zero-crossing method for frequency map analysis of dynamical systems

Author:

Yurin Denis1ORCID,Makukov Maxim1ORCID,Kuvatova Dana1ORCID,Gluchshenko Anton1,Omarov Chingis1

Affiliation:

1. Fesenkov Astrophysical Institute , Observatory 23, Almaty 050020 , Kazakhstan

Abstract

ABSTRACT We present a simple method for estimating fundamental frequencies from orbit’s time series of triaxial dynamical systems based on the zero-crossing technique. The simplicity and high performance of the method make it a viable alternative to more advanced, but rather complex and computationally expensive techniques based on Fourier spectral analysis and iterative torus-mapping with action-angle variables. More importantly, the method provides a simple and quick way to identify irregular orbits and quantify their level of chaoticity, allowing to detect even a subtle onset of chaos. To validate the proposed algorithm, we performed comparison tests with synthetic quasi-periodic signals and with other methods using the triaxial Dehnen potential. We found noticeable differences in frequency maps constructed with our method and methods based on Fourier spectral analysis that we attributed to the way we assign static properties to chaotic orbits. At the same time, our frequency maps turn out to be in very good agreement with the maps obtained using the action-based technique.

Funder

Ministry of Science and Higher Education

Publisher

Oxford University Press (OUP)

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