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Chaos identification through the auto-correlation function indicator (ACFI)

Published online by Cambridge University Press:  30 May 2022

Valerio Carruba Open the ORCID record for Valerio Carruba [Opens in a new window] ,
Safwan Aljbaae ,
Rita C. Domingos ,
Mariela Huaman  and
William Barletta
Valerio Carruba
Affiliation:
São Paulo State University (UNESP), Guaratinguetá, SP, 12516-410, Brazil email: valerio.carruba@unesp.br
Safwan Aljbaae
Affiliation:
National Space Research Institute (INPE), C.P. 515, 12227-310, São José dos Campos, SP, Brazil
Rita C. Domingos
Affiliation:
São Paulo State University (UNESP), São João da Boa Vista, SP, 13876-750, Brazil
Mariela Huaman
Affiliation:
Universidad tecnológica del Perú (UTP), Cercado de Lima, 15046, Perú
William Barletta
Affiliation:
São Paulo State University (UNESP), Guaratinguetá, SP, 12516-410, Brazil email: valerio.carruba@unesp.br
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Abstract

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Close encounters or resonances overlaps can create chaotic motion in small bodies in the Solar System. Approaches that measure the separation rate of trajectories that start infinitesimally near, or changes in the frequency power spectrum of time series, among others, can discover chaotic motion. In this paper, we introduce the ACF index (ACFI), which is based on the auto-correlation function of time series. Auto-correlation coefficients measure the correlation of a time-series with a lagged duplicate of itself. By counting the number of auto-correlation coefficients that are larger than 5% after a certain amount of time has passed, we can assess how the time series auto-correlates with each other. This allows for the detection of chaotic time-series characterized by low ACFI values.

Keywords

Celestial mechanicsAsteroid BeltChaotic MotionsStatistical Methods
Type
Research Article
Information
Proceedings of the International Astronomical Union , Volume 15 , Symposium S364: Multi-scale (Time and Mass) Dynamics of Space Objects (Oct 2021) , October 2019 , pp. 108 - 112
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of International Astronomical Union

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