Asymmetry Coefficients as Indicators of Chaos

P. Wąża and D. Bielińska-Wążb a Centrum Astronomii, Uniwersytet Mikołaja Kopernika, Gagarina 11, 87-100 Toruń, Poland b Instytut Fizyki, Uniwersytet Mikołaja Kopernika, Grudziądzka 5, 87-100 Toruń, Poland

Received: August 11, 2008

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The aim of this paper is to present a new simple indicator of chaos derived from the dynamics of the motion. For this purpose statistical methods are used. A function describing the motion of the analyzed system (in the example under consideration, the time dependence of the angle of a damped driven pendulum, οmega(t)) is recorded in time intervals t∊〈 Ts, Tfk〉, k = 1, 2, ... K, with Tfk > Tfk-1. Each of the recorded functions is considered as a statistical distribution. The asymmetry coefficients of the set of distributions form a series and their behavior in periodic and chaotic regions is compared. It is shown that the behavior of this series in the chaotic and in the periodic regimes is entirely different. The changes of the asymmetry coefficients for the periodic cases are very regular and for the chaotic ones - random. In periodic cases, the coefficients converge to zero when the length of the distribution increases.

DOI: 10.12693/APhysPolA.116.987 PACS numbers: 02.70.Rr, 95.10.Fh, 05.45.-a, 05.45.Gg, 05.45.Tp