Issue |
ESAIM: Proc.
Volume 36, April 2012
European Conference on Iteration Theory 2010
|
|
---|---|---|
Page(s) | 106 - 120 | |
DOI | https://doi.org/10.1051/proc/201236009 | |
Published online | 28 August 2012 |
Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches
1
DESP, University of Urbino, Urbino, Italy
e-mail: laura.gardini@uniurb.it
2
Institute of Parallel and Distributed Systems, University of
Stuttgart, Germany
e-mail: Viktor.Avrutin@ipvs.uni-stuttgart.de,
Michael.Schanz@ipvs.uni-stuttgart.de, Albert
Granados@ipvs.uni-stuttgart.de
3
National Academy of Sciences of Ukraine, and Kiev School of
Economics, Kiev,
Ukraine
e-mail: sushko@imath.kiev.ua
This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where it was proved that in the case of an increasing/decreasing contracting functions on the left/right side of a border point, at such a crossing point, we have a big-bang bifurcation, from which infinitely many border collision bifurcation curves are issuing.
Résumé
Cet travail est une contribution à la classification des comportements dynamiques de systèmes réguliers par morceaux dans lesquels les bifurcations de collision au bord caractérisent les changements qualitatifs de la dynamique. Un point central de notre étude est l’intersection de deux courbes de bifurcation de colision au bord dans un plan de paramètre. Ce problème est aussi associé avec la rupture de continuité en un point fixe d’une application régulière par morceaux. Nous allons relacher l’hypothèse requise dans [4], où il a été montré que dans le cas de fonctions contractantes croissantes/décroissantes strictement à gauche/droite d’un point du bord, en un tel point de franchissement, nous avons une bifurcation big-bang, de laquelle est issue une infinité de courbes de bifurcation de collision au bord.
Mathematics Subject Classification: 37E05 / 37G10 / 37G35
Key words: piecewise smooth maps / border collision bifurcations / organizing centers
Mots clés : applications régulières par morceaux / bifurcations de collision au bord / centres organisateurs
© EDP Sciences, SMAI 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.