An elementary approach to dynamics and bifurcations of skew tent maps
2008 (English)In: Journal of difference equations and applications (Print), ISSN 1023-6198, Vol. 14, no 8, 819-833 p.Article in journal (Refereed) Published
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.
threshold autoregressive model, skew tent map, uniqueness of periodic, attractors, difference equation, chaos, bifurcation diagram, threshold, model
IdentifiersURN: urn:nbn:se:kth:diva-17608DOI: 10.1080/10236190801927462ISI: 000256766900003ScopusID: 2-s2.0-45849154256OAI: oai:DiVA.org:kth-17608DiVA: diva2:335652
QC 201005252010-08-052010-08-05Bibliographically approved