Publications BV: Bibliography 2011 BibTeX
@article {ART-2011-23,
author = {Viktor Avrutin and Albert Granados and Michael Schanz},
title = {{Sufficient conditions for a period increment big bang bifurcation in one-dimensional maps}},
journal = {Nonlinearity},
publisher = {IOP Publishing},
volume = {24},
number = {9},
pages = {2575--2598},
type = {Article in Journal},
month = {August},
year = {2011},
isbn = {10.1088/0951-7715/24/9/012},
keywords = {piecewise smooth discontinuous maps; period incrementing},
language = {English},
cr-category = {J.2 Physical Sciences and Engineering},
ee = {http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=10-124},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding},
abstract = {Typically, big bang bifurcation occur for one (or higher)-dimensional
piecewise-defined systems whenever two border collision bifurcation curves
collide transversely in the parameter space. At that point, two (feasible)
fixed points collide with the boundary in state space and become virtual.
Depending on the properties of the map near the codimension-two bifurcation
point, there exist different scenarios regarding how the infinite number of
periodic orbits are born, mainly the so-called period adding and period
incrementing. In our work we prove that, in order to undergo a big bang
bifurcation of the period incrementing type, it is sufficient for a
piecewise-defined one-dimensional map that the colliding fixed points are
attractive and with associated eigenvalues of different sign},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2011-23&engl=1}
}
@article {ART-2011-09,
author = {Viktor Avrutin and Michael Schanz and Bj{\"o}rn Schenke},
title = {{Coexistence of the Bandcount-Adding and Bandcount-Increment Scenarios}},
journal = {Discrete Dynamics in Nature and Society},
publisher = {Online (Hindawi Publishing Corporation)},
volume = {2011},
number = {Article ID 681565},
pages = {1--30},
type = {Article in Journal},
month = {January},
year = {2011},
doi = {10.1155/2011/681565},
language = {English},
cr-category = {J.2 Physical Sciences and Engineering,
G.2 Discrete Mathematics},
ee = {http://www.hindawi.com/journals/ddns/2011/681565/},
contact = {E-Mail: Bjoern.Schenke@ipvs.uni-stuttgart.de},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding},
abstract = {We investigate the structure of the chaotic domain of a specific
one-dimensional piecewise linear map with one discontinuity. In this system,
the region of {\^a}robust`` chaos is embedded between two periodic domains. One of
them is organized by the period-adding scenario whereas the other one by the
period-increment scenario with coexisting attractors. In the chaotic domain,
the influence of both adjacent periodic domains leads to the coexistence of the
recently discovered bandcount adding and bandcount-increment scenarios. In this
work, we focus on the explanation of the overall structure of the chaotic
domain and a description of the bandcount adding and bandcount increment
scenarios.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2011-09&engl=1}
}
@article {ART-2011-08,
author = {Bj{\"o}rn Schenke and Viktor Avrutin and Michael Schanz},
title = {{On a bifurcation structure mimicking period adding}},
journal = {Proceedings of the Royal Society A},
address = {London},
publisher = {The Royal Society},
volume = {467},
number = {2129},
pages = {1503--1518},
type = {Article in Journal},
month = {May},
year = {2011},
doi = {10.1098/rspa.2010.0573},
keywords = {piecewise smooth systems; border collision bifurcations; simple limiter control; nested period-incrementing bifurcation scenario},
language = {English},
cr-category = {J.2 Physical Sciences and Engineering,
G.2 Discrete Mathematics},
ee = {http://rspa.royalsocietypublishing.org/content/467/2129/1503.abstract},
contact = {E-Mail: Bjoern.Schenke@ipvs.uni-stuttgart.de},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Image Understanding},
abstract = {In this work, we investigate a piecewise-linear discontinuous scalar map
defined on three partitions. This map is specifically constructed in such a way
that it shows a recently discovered bifurcation scenario in its pure form.
Owing to its structure on the one hand and the similarities to the nested
period-adding scenario on the other hand, we denoted the new bifurcation
scenario as nested period-incrementing bifurcation scenario. The new
bifurcation scenario occurs in several physical and electronical systems but
usually not isolated, which makes the description complicated. By isolating the
scenario and using a suitable symbolic description for the asymptotically
stable periodic orbits, we derive a set of rules in the space of symbolic
sequences that explain the structure of the stable periodic domain in the
parameter space entirely. Hence, the presented work is a necessary step for the
understanding of the more complicated bifurcation scenarios mentioned above.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2011-08&engl=1}
}
