False periods in complex chaotic systems

¹ Astronomický ústav, Akademie věd České republiky v.v.i., 251 65 Ondřejov, Czech Republic e-mail: votruba@sunstel.asu.cas.cz
² Ústav teoretické fyziky a astrofyziky, Přirodověcká fakulta, Masarykova univerzita, Kotlářská 2, 611 37 Brno, Czech Republic

Received: 16 October 2008
Accepted: 19 December 2008

Abstract

Aims. 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.

Methods. We analyse the feasibility of classical methods for period searches in a nonlinear chaotic system, such as the Rössler 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.

Results. 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.