On the scaling properties of the period-increment scenario in dynamical systems

Citation
V. Avrutin et M. Schanz, On the scaling properties of the period-increment scenario in dynamical systems, CHAOS SOL F, 11(13), 2000, pp. 1949-1955
Citations number
24
Categorie Soggetti
Multidisciplinary
Journal title
CHAOS SOLITONS & FRACTALS
ISSN journal
09600779 → ACNP
Volume
11
Issue
13
Year of publication
2000
Pages
1949 - 1955
Database
ISI
SICI code
0960-0779(200010)11:13<1949:OTSPOT>2.0.ZU;2-P
Abstract
Two one-dimensional dynamical systems discrete in time are presented, where the variation of one parameter causes a sequence of global bifurcations; a t each bifurcation the period increases by a constant value (period-increme nt scenario, usually denoted as a period-adding scenario). We determine all the bifurcation points and the scaling constants of the period-increment s cenario analytically. A re-injection mechanism, leading to the period-incre ment scenario, is discussed. It will be shown, that in systems with more th an one parameter the scaling constants can depend on the values of the para meters. (C) 2000 Elsevier Science Ltd. All rights reserved.