Introducing nonlinear time series analysis in undergraduate courses

Abstract

This article is written for undergraduate students and teachers who would like to get familiar with basic nonlinear time series analysis methods. We present a step-by-step study of a simple example and provide user-friendly programs that allow an easy reproduction of presented results. In particular, we study an artificial time series generated by the Lorenz system. The mutual information and false nearest neighbour method are explained in detail, and used to obtain the best possible attractor reconstruction. Subsequently, the times series is tested for stationarity and determinism, which are both important properties that assure correct interpretation of invariant quantities that can be extracted from the data set. Finally, as the most prominent invariant quantity that allows distinguishing between regular and chaotic behaviour, we calculate the maximal Lyapunov exponent. By following the above steps, we are able to convincingly determine that the Lorenz system is chaotic directly from the generated time series, without the need to use the differential equations. Throughout the paper, emphasis on clear-cut guidance and a hands-on approach is given in order to make the reproduction of presented results possible also for undergraduates, and thus encourage them to get familiar with the presented theory.

Keywords

nelinearni sistemi;analize časovnih zaporedij;pouk fizike;nonlinear systems;nonlinear time series analyses;physics education;

Data

Language:	English
Year of publishing:	2006
Typology:	1.04 - Professional Article
Organization:	UM PEF - Faculty of Education
UDC:	530.182
COBISS:	15229704
ISSN:	1330-0008
Views:	1179
Downloads:	28
Average score:	0 (0 votes)
Metadata:

Other data

Secondary title:	Uvođenje analize nelinearnih vremenskih nizova u dodiplomski studij
Secondary keywords:	nelinearni sistemi;analize časovnih zaporedij;pouk fizike;
URN:	URN:SI:UM:
Pages:	str. 91-112
Volume:	ǂVol. ǂ15
Issue:	ǂno. ǂ2
Chronology:	2006
ID:	8724211