False periods in complex chaotic systems

TL;DR

This paper investigates the challenges of identifying true periodicity in chaotic stellar light curves, demonstrating that classical period search methods often produce spurious periods in chaotic systems.

Contribution

It evaluates the effectiveness of traditional period analysis techniques on chaotic stellar models, highlighting their limitations in distinguishing chaos from quasiperiodicity.

Findings

Classical methods often detect false periods in chaotic signals.

Chaotic and quasiperiodic signals can appear similar in period analysis.

Distinguishing chaos from periodicity requires more than standard period searches.

Abstract

Astrophysical objects frequently exhibit some irregularities or complex behaviour in their light curves. We focus primarily on hot stars, where both radial and non-radial pulsations are observed. One of the primary research goals is to determine physical parameters of stellar pulsations by analyzing their light curves or spectra, focusing on periodic or quasiperiodic behaviour. We analyse the feasibility of classical methods for period searches in a nonlinear chaotic system, such as the R\"ossler system, where a period does not exist at all. As an astrophysical application of the chaotic system, we utilize a simple model of stellar pulsation with two different sets of parameters corresponding to periodic and chaotic behaviour. For both models we create a synthetic signal, and then apply widely used methods for period finding, such as the phase dispersion method and periodograms. For comparison, a quasi-periodic signal is employed as well. The period analysis indicates periods even for the chaotic signal. Such periods are apparently spurious. This implies that it is very problematic to distinguish chaotic and quasiperiodic process by such an analysis only.