Artikel in Zeitschrift ART-2010-19

Bibliograph.
Daten
Avrutin, Viktor; Schanz, Michael; Gardini, Laura: Self-similarity of the bandcount adding structures: Calculation by map replacement.
In: Regular and Chaotic Dynamics. Vol. 15(6).
Universität Stuttgart, Fakultät Informatik, Elektrotechnik und Informationstechnik.
S. 658-703, englisch.
Springer Verlag, Dezember 2010.
DOI: 10.1134/S1560354710060055.
Artikel in Zeitschrift.
CR-Klassif.J.2 (Physical Sciences and Engineering)
Keywordspiecewise-linear maps, crisis bifurcations, chaotic attractors, bandcount adding and doubling, self-similarity, renormalization
Kurzfassung

Recently it has been 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 usually a quite sophisticated and cumbersome task. In this work we demonstrate that, using the map replacement approach, the bifurcation curves can be calculated much easier. Moreover, using this approach recursively, we confirm the hypothesis regarding the self-similarity of the bandcount adding structure.

Abteilung(en)Universität Stuttgart, Institut für Parallele und Verteilte Systeme, Bildverstehen
Projekt(e)Organisationszentren in nichtglatten dynamischen Systemen: Bifurkationen höherer Kodimension in Theorie und Anwendungen
AnT 4.669
Eingabedatum26. Januar 2011
   Publ. Institut   Publ. Informatik