Article in Journal ART-2010-18

BibliographyGardini, Laura; Tramontana, Fabio; Avrutin, Viktor; Schanz Michael: Border-Collision Bifurcations in 1D Piecewise-Linear Maps and Leonov's Approach.
In: International Journal of Bifurcation and Chaos. Vol. 20(10).
University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology.
pp. 3085-3104, english.
World Scientific Publishing Company, December 2010.
DOI: 10.1142/S021812741002757X.
Article in Journal.
CR-SchemaJ.2 (Physical Sciences and Engineering)
KeywordsDiscontinuous piecewise-linear 1D maps; border collision bifurcations; adding mechanism; Farey structure
Abstract

50 years ago (1959) in a series of publications by Leonov, a detailed analytical study of the nested period adding bifurcation structure occurring in piecewise-linear discontinuous 1D maps was presented. The results obtained by Leonov are barely known, although they allow the analytical calculation of border-collision bifurcation subspaces in an elegant and much more efficient way than it is usually done. In this work we recall Leonov's approach and explain why it works. Furthermore, we slightly improve the approach by avoiding an unnecessary coordinate transformation, and also demonstrate that the approach can be used not only for the calculation of border-collision bifurcation curves.

Department(s)University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding
Project(s)Organisationszentren in nichtglatten dynamischen Systemen: Bifurkationen höherer Kodimension in Theorie und Anwendungen
AnT 4.669
Entry dateJanuary 26, 2011
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