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An elementary approach to dynamics and bifurcations of skew tent maps
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7158-5865
2008 (English)In: Journal of difference equations and applications (Print), ISSN 1023-6198, E-ISSN 1563-5120, Vol. 14, no 8, 819-833 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, the dynamics of skew tent maps are classified in terms of two bifurcation parameters. In time series analysis such maps are usually referred to as continuous threshold autoregressive models (TAR(1)-models) after Tong (Non-Linear Time Series, Clarendon Press, Oxford, UK, 1990). This study contains results simplifying the use of TAR(1)-models considerably, e.g. if a periodic attractor exists it is unique. On the other hand, we also claim that care must be exercised when TAR models are used. In fact, they possess a very special type of dynamical pattern with respect to the bifurcation parameters and their transition to chaos is far from standard.

Place, publisher, year, edition, pages
2008. Vol. 14, no 8, 819-833 p.
Keyword [en]
threshold autoregressive model, skew tent map, uniqueness of periodic, attractors, difference equation, chaos, bifurcation diagram, threshold, model
Identifiers
URN: urn:nbn:se:kth:diva-17608DOI: 10.1080/10236190801927462ISI: 000256766900003Scopus ID: 2-s2.0-45849154256OAI: oai:DiVA.org:kth-17608DiVA: diva2:335652
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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