Embedding and Time Series Analysis

Huke, Jeremy P. and Muldoon, Mark R. (2015) Embedding and Time Series Analysis. Mathematics Today, 51 (3). pp. 120-123. ISSN 1361-2042

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Abstract

The 1970's and 80's saw a tremendous wave of interest---across the sciences and beyond---in the subject of nonlinear dynamics. Under the heading of `chaos theory' the subject even gripped the public imagination, leading to popular books and television programmes and even a mention in the film \emph{Jurassic Park}. One of the central ideas driving this interest was the realization that the complex, unpredictable behaviour known as chaos might be widespread in physical systems, and possibly even in biological, economic and social systems as well. This kind of behaviour, with its characteristic \emph{sensitive dependence on initial conditions}, had been shown to occur in a range of simple mathematical systems, many of which were conceived as models of physical or biological phenomena. As well as triggering much work on the mathematical theory of nonlinear dynamical systems, this also raised the intriguing question of whether chaotic behaviour could actually be observed in the broad range of experimental situations that the simple models hinted at. But while physicists and engineers were very familiar with experiments designed to investigate the various periodicities within a system, how should they treat the experimental data (or devise the experiments themselves) so as to reveal the characteristic features of chaos, such as the aforementioned sensitive dependence on initial conditions, or the strange attractors, with their fractal structures, that live in the state spaces of some chaotic systems?

Item Type: Article
Uncontrolled Keywords: nonlinear dynamics, delay embedding
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 57 Manifolds and cell complexes
MSC 2010, the AMS's Mathematics Subject Classification > 92 Biology and other natural sciences
MSC 2010, the AMS's Mathematics Subject Classification > 93 Systems theory; control
Depositing User: Dr Mark Muldoon
Date Deposited: 26 Sep 2016
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2504

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