Article in Proceedings INPROC-2009-107

BibliographyAvrutin, Viktor; Schanz, Michael: Self-similarity of the bandcount adding: calculation by map replacement.
In: University of Urbino, Italy (ed.); INSA Toulouse, France (ed.); Tokushima University, Japan (ed.): Proceedings of the 2009 International Workshop on Nonlinear Maps and their Applications (NOMA'09).
University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology.
pp. 62-66, english.
University of Urbino, INSA Toulouse, Tokushima University, September 2009.
Article in Proceedings (Conference Paper).
CR-SchemaG.1.0 (Numerical Analysis General)
J.2 (Physical Sciences and Engineering)
Keywordsmulti-band chaotic attractors; discontinuous maps; bandcount adding
Abstract

Recently it was demonstrated that the domain of robust chaos close to the periodic domain, which is organized by the period-adding structure, contains an infinite number of interior crisis bifurcation curves. These curves form the so-called bandcount adding scenario, which determines the occurrence of multi-band chaotic attractors. The analytical calculation of the interior crisis bifurcations represents a quite sophisticated task. In this work we demonstrate that, using the map replacement approach, much more bifurcation curves can be calculated. Moreover, using this approach recursively, we confirm the hypothesis regarding the self-similarity of the bandcount adding structure.

Department(s)University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding
Project(s)AnT
OCiND
Entry dateDecember 10, 2009
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