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Title:
Introducing nonlinear time series analysis in undergraduate courses
Authors:
ID
Perc, Matjaž
(Author)
Files:
http://fizika.hfd.hr/fizika_a/av06/a15p091.htm
Language:
English
Work type:
Unknown
Typology:
1.04 - Professional Article
Organization:
PEF - Faculty of Education
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:
nonlinear systems
,
nonlinear time series analyses
,
physics education
Year of publishing:
2006
PID:
20.500.12556/DKUM-35975
UDC:
530.182
ISSN on article:
1330-0008
COBISS.SI-ID:
15229704
NUK URN:
URN:SI:UM:DK:MEUXN440
Publication date in DKUM:
07.06.2012
Views:
2089
Downloads:
37
Metadata:
Categories:
Misc.
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PERC, Matjaž, 2006, Introducing nonlinear time series analysis in undergraduate courses.
Fizika
[online]. 2006. [Accessed 2 April 2025]. Retrieved from: http://fizika.hfd.hr/fizika_a/av06/a15p091.htm
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Record is a part of a journal
Title:
Fizika
Shortened title:
Fiz. A
Publisher:
Croatian Physical Society
ISSN:
1330-0008
COBISS.SI-ID:
31589121
Secondary language
Language:
Croatian
Title:
Uvođenje analize nelinearnih vremenskih nizova u dodiplomski studij
Keywords:
nelinearni sistemi
,
analize časovnih zaporedij
,
pouk fizike
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