Asymmetry Coefficients as Indicators of Chaos

• Authors: P. Wąż , D. Bielińska-Wąż
• Languages of publication: EN

Abstracts

EN

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, ω(t)) is recorded in time intervals t∊〈 T_{s}, T_{f_{k}}〉, k = 1, 2,...K, with T_{f_{k}} > T_{f_{k-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.

Keywords

EN

02.70.Rr; 95.10.Fh; 05.45.-a; 05.45.Gg; 05.45.Tp

Discipline

• 05.45.-a: Nonlinear dynamics and chaos(see also section 45 Classical mechanics of discrete systems; for chaos in fluid dynamics, see 47.52.+j; for chaos in superconductivity, see 74.40.De)
• 05.45.Gg: Control of chaos, applications of chaos
• 05.45.Tp: Time series analysis
• 95.10.Fh: Chaotic dynamics(see also 05.45.-a Nonlinear dynamics and chaos)
• 02.70.Rr: General statistical methods

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2009
• Volume: 116
• Issue: 6
• Pages: 987-991

Dates

published

2009-12

received

2008-08-11

Contributors

author

P. Wąż

• Centrum Astronomii, Uniwersytet Mikołaja Kopernika, Gagarina 11, 87-100 Toruń, Poland

author

D. Bielińska-Wąż

• Instytut Fizyki, Uniwersytet Mikołaja Kopernika, Grudziądzka 5, 87-100 Toruń, Poland

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Identifiers

DOI

10.12693/APhysPolA.116.987