@inproceedings {INPROC-2009-43,
author = {Partha Dutta and Viktor Avrutin and Michael Schanz and Soumitro Banerjee},
title = {{Multi-parametric bifurcations in a piecewise smooth map with square-root singularity}},
booktitle = {Proceedings of the National Conference on Nonlinear Systems \& Dynamics, Saha Institute of Nuclear Physics, Kolkota, India, March 5-7, 2009},
publisher = {Online},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {1--1},
type = {Konferenz-Beitrag},
month = {M{\"a}rz},
year = {2009},
keywords = {piecewise smooth map; multi-parametric bifurcation},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering},
ee = {http://www.cts.iitkgp.ernet.in/~ncnsd/Proceedings09/Paper/10.pdf},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {Considering the concept of multi-parametric bifurcations, the piecewise smooth
linear normal form map can exhibit many typical bifurcation phenomena, which
can not be observed in smooth dynamical systems. In this paper we investigate
especially the interaction between smooth and non-smooth bifurcations in the
multi-parametric domain.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2009-43&engl=0}
}
@inproceedings {INPROC-2009-134,
author = {Laura Gardini and Fabio Tramontana and Viktor Avrutin and Michael Schanz},
title = {{Improvment of the Leonov approach for border collision bifurcation curves}},
booktitle = {Proceedings of the 2009 International Workshop on Nonlinear Maps and their Applications (NOMA'09)},
publisher = {University of Urbino, INSA Toulouse, Tokushima University},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {43--46},
type = {Konferenz-Beitrag},
month = {September},
year = {2009},
keywords = {Border-collision bifurcations; Piecewise-smooth maps; Piecewise-linear maps},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering,
G.2 Discrete Mathematics},
contact = {Viktor.Avrutin@ipvs.uni-stuttgart.de Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {The study of bifurcations in a piecewise-smooth system is quite different from
those occurring in smooth systems. In piecewise-linear systems, which we are
considering in this paper, mainly border collision bifurcations (BCBs) and
contact bifurcations occur. It is classified as border-collision any contact
between an invariant set of a map with the border of its region of definition,
and this may, or may not, produce a bifurcation. The term border-collision
bifurcation was introduced for the first time by Nusse and Yorke in 1992 and is
now widely used in this context (i.e. for piecewise smooth maps). Recently,
these bifurcations have been studied mainly because of their relevant
applications in engineering (electrical and mechanical), and also in economics
and social sciences. In fact, several publications were motivated by models
describing particular circuits or models for the transmission of signals.
Remarkably also before the work by Nusse and Yorke the bifurcations associated
with piecewise smooth maps were studied in some publications (although the
bifurcations were not called border-collision bifurcations). We recall, for
example, the works by Mira (1978) and others. We may also go further back,
citing the work by Leonov in the end of 50th. In his work, Leonov described
several bifurcations, giving a recurrence relation to find the analytic
expressions of families of bifurcations occurring in a one-dimensional
piecewise linear map with one point of discontinuity, which is still mainly
unknown. The object of this work is to give a new interpretation and
improvements of some of his results.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2009-134&engl=0}
}
@inproceedings {INPROC-2009-133,
author = {Viktor Avrutin and Michael Schanz and Bj{\"o}rn Schenke},
title = {{On a bifurcation structure mimicking period adding}},
booktitle = {Proceedings of the 2009 International Workshop on Nonlinear Maps and their Applications (NOMA'09)},
publisher = {University of Urbino, INSA Toulouse, Tokushima University},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {72--77},
type = {Konferenz-Beitrag},
month = {September},
year = {2009},
keywords = {Border-collision bifurcations; Piecewise-smooth maps; Piecewise-linear maps},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering,
G.2 Discrete Mathematics},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work we investigate a piecewise-linear dis- continuous map defined on
three partitions. This map denoted as truncated tent map was specifically
constructed in such a way that it shows a similar dynamic behavior like a
piecewise- linear continuous map with an additional square root term with
positive sign derived from the time continuous model of an impact oscillator.
Since the square root part makes analytical studies complicated, the
constructed map serves us as an easy to investigate test system. The stable
periodic dynamics of this piecewise-linear map was found to be organized by a
heretofore unexplained bifurcation structure in an extended region in parameter
space, which superficially resembles period adding. This work explains the
stable periodic behavior of the truncated tent map and the new bifurcation
structure.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2009-133&engl=0}
}
@inproceedings {INPROC-2009-132,
author = {Viktor Avrutin and Michael Schanz and Bj{\"o}rn Schenke},
title = {{Floating regions within robust chaos}},
booktitle = {Proceedings of the 2009 International Workshop on Nonlinear Maps and their Applications (NOMA'09)},
publisher = {University of Urbino, INSA Toulouse, Tokushima University},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {67--71},
type = {Konferenz-Beitrag},
month = {September},
year = {2009},
keywords = {Crisis bifurcations; Piecewise-smooth maps; Piecewise-linear maps},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering,
G.2 Discrete Mathematics},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {When dealing with piecewise-smooth systems, the chaotic domain is often robust,
that means does not contain any periodic inclusions. Recently, the bifurcation
structures in the robust chaotic domain of 1D piecewise-linear maps was
investigated. It was shown that several regions of multi-band chaotic
attractors emerge at the boundary between the periodic and the chaotic domain,
forming complex self-similar bifurcation structures. However, some multi-band
regions were observed also far away from this boundary. In this work we
consider the question how these regions emerge and how they become disconnected
from the boundary.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2009-132&engl=0}
}
@inproceedings {INPROC-2009-131,
author = {Viktor Avrutin and Michael Schanz and Laura Gardini},
title = {{Map replacement approach for calculation of bifurcation curves and its applicability conditions}},
booktitle = {Proceedings of the 2009 International Workshop on Nonlinear Maps and their Applications (NOMA'09)},
publisher = {University of Urbino, INSA Toulouse, Tokushima University},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {53--58},
type = {Konferenz-Beitrag},
month = {September},
year = {2009},
keywords = {Border-collision bifurcations; Piecewise-smooth maps; Piecewise-linear maps},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering,
G.2 Discrete Mathematics},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work we reconsider the approach suggested about 50 years ago (1959) in
a series of publications by N.N.Leonov for the calculation of border-collision
bifurcation curves in piecewise-linear maps. We extend this approach and
explain its applicability conditions.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2009-131&engl=0}
}
@inproceedings {INPROC-2009-107,
author = {Viktor Avrutin and Michael Schanz},
title = {{Self-similarity of the bandcount adding: calculation by map replacement}},
booktitle = {Proceedings of the 2009 International Workshop on Nonlinear Maps and their Applications (NOMA'09)},
editor = {Italy University of Urbino and France INSA Toulouse and Japan Tokushima University},
publisher = {University of Urbino, INSA Toulouse, Tokushima University},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {62--66},
type = {Konferenz-Beitrag},
month = {September},
year = {2009},
keywords = {multi-band chaotic attractors; discontinuous maps; bandcount adding},
language = {Englisch},
cr-category = {G.1.0 Numerical Analysis General,
J.2 Physical Sciences and Engineering},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
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.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2009-107&engl=0}
}
@inproceedings {INPROC-2008-80,
author = {Viktor Avrutin and Michael Schanz},
title = {{Crises cascades within robust chaos in piecewise-smooth maps}},
booktitle = {Proceedings of the 6th EUROMECH Nonlinear Dynamics Conference},
publisher = {European Mechanics Society},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {1--6},
type = {Konferenz-Beitrag},
month = {Juli},
year = {2008},
keywords = {crises bifurcations; multi-band chaotic attractors; bandcount adding scenario},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {This article describes a novel bifurcation phenomenon occurring in the 2D
parameter space of piecewise-linear maps. In the region of chaotic behavior we
detect an infinite number of interior crises bounding the regions of multi-band
attractors. This phenomenon, denoted as bandcount adding scenario, leads to a
self-similar structure of the chaotic region in the parameter space.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2008-80&engl=0}
}
@inproceedings {INPROC-2008-142,
author = {Laura Gardini and Viktor Avrutin and Michael Schanz},
title = {{Connection between bifurcations on the Poincare Equator and the dangerous bifurcations}},
booktitle = {Book of Abstracts: European Conference on Iteration Theory: Yalta, Crimea, Ukraine, September 7-13, 2008},
publisher = {Institute of Mathematics, National Academy of Sciences of Ukraine},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {1--1},
type = {Konferenz-Beitrag},
month = {September},
year = {2008},
keywords = {border collision bifurcation; dangerous bifurcation; Poincare equator},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering,
G.2 Discrete Mathematics},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {The object of the present work is to describe some bifurcations occurring in
the 2D piecewise linear continuous map in canonical form involving the Poincare
Equator (i.e. periodic points at infinity) and its relation to the so called
``dangerous bifurcations'' (following Hassouneh et al. [2004] and Ganguli and
Banerjee [2005]). It will be shown that such regions are related not only to
stable fixed points and repelling saddle cycles, and a more general definition
is proposed. The boundaries of such regions are border collision bifurcations
of cycles on the Poincare Equator.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2008-142&engl=0}
}
@inproceedings {INPROC-2008-114,
author = {Oliver Zweigle and Uwe-Philipp K{\"a}ppeler and Hamid Rajaie and Kai H{\"a}u{\ss}ermann and Reinhard Lafrenz and Andreas Tamke and Frank Schreiber and Markus H{\"o}ferlin and Michael Schanz and Paul Levi},
title = {{CoPS Stuttgart Team Description 2008}},
booktitle = {Proceedings of the RoboCup International Symposium; Suzhou, China, July 14-20, 2008},
address = {Suzhou},
publisher = {RoboCup Organization},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {1--8},
type = {Konferenz-Beitrag},
month = {Juli},
year = {2008},
keywords = {Robot soccer},
language = {Englisch},
cr-category = {I.2.9 Robotics,
I.2.10 Vision and Scene Understanding,
I.2.11 Distributed Artificial Intelligence,
I.2 Artificial Intelligence},
ee = {http://robocup.informatik.uni-stuttgart.de/,
www.robocup.org},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {The CoPS robot soccer team is used as a testbed for multi-agent software
architecture principles in dynamic real time domains. The current research
activities focus on a new controlling architecture, rein- forcement learning
for robot behaviors, situation recognition and new vison methots.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2008-114&engl=0}
}
@inproceedings {INPROC-2008-104,
author = {Reinhard Lafrenz and Michael Schanz and Uwe-Philipp K{\"a}ppeler and Oliver Zweigle and Hamid Rajaie and Frank Schreiber and Paul Levi},
title = {{Evaluating Robustness of Coupled Selection Equations Using Sparse Communication}},
booktitle = {Intelligent Autonomous Systems 10 (IAS-10)},
editor = {Burgard et al.},
publisher = {IOS Press},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {272--277},
type = {Konferenz-Beitrag},
month = {Juli},
year = {2008},
language = {Englisch},
cr-category = {I.2.9 Robotics,
I.2.11 Distributed Artificial Intelligence,
G.1.10 Numerical Analysis Applications},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this paper we evaluate the robustness of a self-organized mechanism to
distribute roles among a team of cooperating robots. In previous work, we
showed the principal applicability of this approach for the RoboCup scenario.
Now we test the robustness in case of either intentionally sparse communication
or the behavior in situations, where the communication is massively disturbed.
To overcome the problems caused by this, each robot runs the equations
individually, synchronizing from time to time, or when the communication is
available.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2008-104&engl=0}
}
@inproceedings {INPROC-2007-75,
author = {Oliver Zweigle and Uwe-Philipp K{\"a}ppeler and Thomas R{\"u}hr and Kai H{\"a}u{\ss}ermann and Reinhard Lafrenz and Frank Schreiber and Andreas Tamke and Hamid Rajaie and Avinash Burla and Michael Schanz and Paul Levi},
title = {{CoPS Stuttgart Team Description 2007}},
booktitle = {Proceedings of the RoboCup International Symposium; Atlanta, Georgia, July 9-10, 2007},
address = {Atlanta},
publisher = {RoboCup Organization},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {1--8},
type = {Konferenz-Beitrag},
month = {Juli},
year = {2007},
keywords = {Robot soccer},
language = {Englisch},
cr-category = {I.2.9 Robotics,
I.2.10 Vision and Scene Understanding,
I.2.11 Distributed Artificial Intelligence,
I.2 Artificial Intelligence},
ee = {http://robocup.informatik.uni-stuttgart.de/,
www.robocup.org},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {The CoPS robot soccer team is used as a testbed for multiagent software
architecture principles in dynamic real time domains. The current research
activities focus on reliable fast communication, situation recognition,
communication and reliable ball detection.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2007-75&engl=0}
}
@inproceedings {INPROC-2007-47,
author = {Reinhard Lafrenz and Frank Schreiber and Oliver Zweigle and Michael Schanz and Hamid Rajaie and Uwe-Philipp K{\"a}ppeler and Paul Levi and Jens Starke},
title = {{Evaluating coupled selection equations for dynamic task assignment using a behavior framework}},
booktitle = {Autonome Mobile Systeme 2007},
editor = {K. Berns and T. Luksch},
address = {Berlin,Heidelberg},
publisher = {Springer-Verlag},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
series = {Informatik Aktuell},
pages = {118--125},
type = {Konferenz-Beitrag},
month = {Oktober},
year = {2007},
isbn = {978-3-540-74763-5},
issn = {1431-472-X},
language = {Englisch},
cr-category = {I.2.9 Robotics,
I.2.11 Distributed Artificial Intelligence},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this paper we focus on methods for a reliable and robust mechanism to
distribute roles among a team of cooperating robots. In previous work, we
showed the principal applicability of a novel approach based on self
organization using coupled selection equations. To show the applicability in
the robocup scenario we used a simple scenario to assign the roles attacker and
defender. In this paper we present the application of the novel approach to
more realistic and complex scenarios like kick-off or pass play. One of the
critical parts in this method is the parameterization of utility and activation
functions used to determine the additional parameters.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2007-47&engl=0}
}
@inproceedings {INPROC-2007-102,
author = {Michael Schanz and Viktor Avrutin},
title = {{On some generic types of discontinuity induced codimension-3 bifurcations.}},
booktitle = {Abstracts for ICIAM 07},
publisher = {Online},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {312--312},
type = {Konferenz-Beitrag},
month = {Juli},
year = {2007},
language = {Englisch},
cr-category = {G.1.10 Numerical Analysis Applications},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work we consider two families of piecewise-linear maps with a
discontinuity, which is motivated by modeling of several power electronic
circuits (DC/DC converters, Sigma-Delta modulators) and which is already
investigated by many authors. However, the focus of these works lie on the
investigation of the dynamics by variation of one or at most two system
parameters. In many of these publications a great variety of bifurcation
phenomena is revealed but unfortunately, a profound explanation of the
complicated and often self-similar bifurcation structures and the systematics
behind is missing. In contrast to that, we investigate the full 3D parameter
space of these families of systems and detect a number of discontinuity induced
codimension-3 bifurcations. Some of them belong to an already known generic
type [1,2], while others represent some new types not investigated so far.
Unfolding these bifurcations we are able to explain the systematics for a large
number of the above mentioned bifurcation phenomena. In particular, several
bifurcation scenarios observed under variation of one or two parameters
represent an intersection of the extended bifurcation structures induced by
codimension-3 bifurcation with the corresponding 1D or 2D parameter subspace.
The codimension-3 bifurcations reported here are characterized by two manifolds
in the 3D parameter space, a 1D and a 2D one. The 1D manifold represents a
codimension-2 bifurcation curve, whereas in the 2D manifold an infinite number
of codimension-2 bifurcation curves are located. At the codimension-3
bifurcation point all these curves intersect. The reported bifurcations serve
as organizing centers of periodic and aperiodic dynamics in the overall
parameter space. [1] V. Avrutin and M. Schanz, Nonlinearity 19, 531 (2006). [2]
V. Avrutin, M. Schanz, and S. Banerjee, Nonlinearity 19, 1875 (2006).},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2007-102&engl=0}
}
@inproceedings {INPROC-2007-101,
author = {Viktor Avrutin and Michael Schanz},
title = {{On the bandcount adding bifurcation scenario.}},
booktitle = {Abstracts for ICIAM07},
publisher = {Online},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {312--312},
type = {Konferenz-Beitrag},
month = {Juli},
year = {2007},
language = {Englisch},
cr-category = {G.1.10 Numerical Analysis Applications},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {An aperiodic and especially a chaotic attractor may consist of some number K $>$=
1 of bands (also denoted as connected components). Multi-band chaotic
attractors (MBCAs) defined by the bandcount K $>$ 1, represent a well-known
phenomenon on the field of nonlinear dynamics and are often involved in several
bifurcations. It is for instance well-known, that the period doubling cascade
is typically followed by an inverse band merging cascade, which represents a
sequence of MBCAs with p0 2^n bands, whereby n decreases from infinity to zero.
We report a novel bifurcation scenario (bandcount adding scenario), which
involves an infinite number of MBCAs organized not sequentially, but according
to an infinite adding scheme. This adding scheme which is similar to the
well-known Farey-trees, implies that between two MBCAs with bandcounts K1 and
K2 there is an MBCA with K1 + K2 - K0 bands (with some constant offset K0).
This scenario continues ad infinitum and resembles the period adding scenario
known from many applications, but in contrast to this is formed by chaotic and
not by periodic attractors. We study this scenario using a discontinuous map,
which is actually considered by many authors as some kind of normal form of the
discrete-time representation of many non-smooth systems of practical interest
in the neighborhood of the point of discontinuity. By investigation of the
structure of the 2D parameter space, we find out, that the bandcount adding
scenario is related with discontinuityinduced codimension-1 bifurcations of
unstable periodic orbits and with some specific discontinuity-induced
codimension-2 bifurcations. Consequently, we describe the self-similarity of
the chaotic area in parameter space and show, that in this area there are much
more non-robust chaotic attractors than typically assumed.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2007-101&engl=0}
}
@inproceedings {INPROC-2005-80,
author = {Mohamed Oubbati and Michael Schanz and Paul Levi},
title = {{Mobile Robot Motion using Neural Networks: An Overview}},
booktitle = {Autonome Mobile Systeme 2005 (AMS)},
editor = {P. Levi and Schanz M. and et. al},
address = {Berlin, Heidelberg, New York},
publisher = {Springer-Verlag},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
series = {Informatik Aktuell},
pages = {303--309},
type = {Konferenz-Beitrag},
month = {Dezember},
year = {2005},
isbn = {978-3-540-30291-9},
keywords = {neural network, mobile robot control},
language = {Englisch},
cr-category = {I.2.8 Problem Solving, Control Methods, and Search},
contact = {Mohamed.Oubbati@informatik.uni-stuttgart.de Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this paper, we provide a summary of our recent results in motion control of
mobile robots using recurrent neural networks. The most important asociated
problems are discussed.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2005-80&engl=0}
}
@inproceedings {INPROC-2005-34,
author = {Mohamed Oubbati and Paul Levi and Michael Schanz},
title = {{Meta-learning for Adaptive Identification of Non-linear Dynamical Systems.}},
booktitle = {Proceedings of the Joint 20th IEEE International Symposium on Intelligent Control \& 13th Mediterranean Conference on Control and Automation (2005 ISIC-MED).},
address = {Limassol, Cyprus},
publisher = {IEEE},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {473--478},
type = {Konferenz-Beitrag},
month = {Juni},
year = {2005},
keywords = {Adaptive Identification; RNNs; Non-linear Dynamical Systems; Meta-learning.},
language = {Englisch},
cr-category = {I.2.8 Problem Solving, Control Methods, and Search},
contact = {Mohamed.Oubbati@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {Adaptive Identification of Non-linear Dynamical Systems via Recurrent Neural
Networks (RNNs) is presented in this paper. We explore the notion that a
fixed-weight RNN needs to change only its internal state to change its behavior
policy. This ability is acquired through prior training procedure that enable
the learning of adaptive behaviors. Some simulation results are presented.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2005-34&engl=0}
}
@inproceedings {INPROC-2005-20,
author = {Mohamed Oubbati and Paul Levi and Michael Schanz},
title = {{A Fixed-Weight RNN Dynamic Controller for Multiple Mobile Robots}},
booktitle = {Proceedings of the 24th IASTED International Conference on MODELLING, IDENTIFICATION, AND CONTROL: MIC 2005; Innsbruck, Austria, February 16-18, 2005.},
address = {Austria},
publisher = {ACTA Press},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
pages = {277--282},
type = {Konferenz-Beitrag},
month = {Februar},
year = {2005},
keywords = {Mobile Robot; Recurrent Neural Networks, Meta-Learning; Adaptive Control},
language = {Englisch},
cr-category = {I.2.9 Robotics},
contact = {Mohamed.Oubbati@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this paper, we demonstrate the ability of a single fixed-weight RNN to act
as a dynamic controller for several (here 3) distinct wheeled mobile robots,
without exact knowledge about their dynamics parameters. The controller is
properly trained to exhibit adaptive behaviour after its weights have been
fixed. This capability is a natural consequence of prior meta-learning used
recently in the area of RNNs.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2005-20&engl=0}
}
@article {ART-2012-20,
author = {Viktor Avrutin and Ben Futter and Laura Gardini and Michael Schanz},
title = {{Unstable Orbits and Milnor Attractors in the Discontinuous Flat Top Tent Map}},
journal = {ESAIM: Proceedings},
publisher = {EDP Sciences},
volume = {36},
pages = {126--158},
type = {Artikel in Zeitschrift},
month = {April},
year = {2012},
doi = {10.1051/proc/201236011},
keywords = {piecewise-smooth maps; discontinuous flat top tent map; maps with a horizontal part; nested period incrementing; Milnor attractors; U-sequence},
language = {Englisch},
cr-category = {G.2 Discrete Mathematics},
ee = {ftp://ftp.informatik.uni-stuttgart.de/pub/library/ncstrl.ustuttgart_fi/ART-2012-20/ART-2012-20.pdf},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work we consider the discontinuous flat top tent map which represents
an example for discontinuous piecewise-smooth maps, whereby the system function
is constant on some interval. Such maps show several characteristics caused by
this constant value which are still insufficiently investigated. In this work
we demonstrate that in the discontinuous flat top tent map every unstable
periodic orbit may become a Milnor attractor. Moreover, it turns out that there
exists a strong connection between stable and unstable orbits and that the
appearance of a single unstable orbit may cause an infinite number of stable
orbits to appear. Based on this connection we provide a more precise
explanation of the recently discovered self-similar bifurcation scenario
occurring in the discontinuous flat top tent map denoted as the nested period
incrementing scenario.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2012-20&engl=0}
}
@article {ART-2012-05,
author = {Ben Futter and Viktor Avrutin and Michael Schanz},
title = {{The discontinuous flat top tent map and the nested period incrementing bifurcation structure}},
journal = {Chaos, Solitons \& Fractals},
publisher = {Elsevier},
volume = {45},
number = {4},
pages = {465--482},
type = {Artikel in Zeitschrift},
month = {April},
year = {2012},
doi = {10.1016/j.chaos.2012.01.009},
issn = {0960-0779},
keywords = {discontinuous flat top tent map; nested period incrementing; symbolic dynamics; U-sequence; discontinuous maps},
language = {Englisch},
cr-category = {G.2.0 Discrete Mathematics General,
J.2 Physical Sciences and Engineering},
ee = {ftp://ftp.informatik.uni-stuttgart.de/pub/library/ncstrl.ustuttgart_fi/ART-2012-05/ART-2012-05.pdf,
http://dx.doi.org/10.1016/j.chaos.2012.01.009},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work we report the recently discovered nested period incrementing
bifurcation scenario. The investigated piecewise linear map is defined on three
partitions of the unit interval, constant in the middle partition and therefore
displays a rich variety of superstable orbits. These orbits are arranged
according to an infinite binary tree of the corresponding symbolic sequences,
which can be generated by a simple set of rules. The system also allows for
straightforward computation of the respective regions of existence. One of the
most striking results of our investigations is that the famous U-sequence is
inevitably embedded in the nested period incrementing scenario.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2012-05&engl=0}
}
@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 = {Artikel in Zeitschrift},
month = {August},
year = {2011},
isbn = {10.1088/0951-7715/24/9/012},
keywords = {piecewise smooth discontinuous maps; period incrementing},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering},
ee = {http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=10-124},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
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=0}
}
@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 = {Artikel in Zeitschrift},
month = {Januar},
year = {2011},
doi = {10.1155/2011/681565},
language = {Englisch},
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 = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
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}€śrobust`` 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=0}
}
@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 = {Artikel in Zeitschrift},
month = {Mai},
year = {2011},
doi = {10.1098/rspa.2010.0573},
keywords = {piecewise smooth systems; border collision bifurcations; simple limiter control; nested period-incrementing bifurcation scenario},
language = {Englisch},
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 = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
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=0}
}
@article {ART-2010-19,
author = {Viktor Avrutin and Michael Schanz and Laura Gardini},
title = {{Self-similarity of the bandcount adding structures: Calculation by map replacement}},
journal = {Regular and Chaotic Dynamics},
publisher = {Springer Verlag},
volume = {15},
number = {6},
pages = {658--703},
type = {Artikel in Zeitschrift},
month = {Dezember},
year = {2010},
doi = {10.1134/S1560354710060055},
keywords = {piecewise-linear maps, crisis bifurcations, chaotic attractors, bandcount adding and doubling, self-similarity, renormalization},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {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.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2010-19&engl=0}
}
@article {ART-2010-17,
author = {Viktor Avrutin and Michael Schanz and Laura Gardini},
title = {{Calculation of Bifurcation Curves by Map Replacement}},
journal = {International Journal of Bifurcation and Chaos},
publisher = {World Scientific Publishing Company},
volume = {20},
number = {10},
pages = {3105--3135},
type = {Artikel in Zeitschrift},
month = {Dezember},
year = {2010},
doi = {10.1142/S0218127410027581},
keywords = {Discontinuous piecewise-linear 1D map; border collision bifurcation curves; map replacement technique; rested period adding; Farey structure.},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering},
contact = {Viktor.Avrutin@ipvs.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {The complex bifurcation structure in the parameter space of the general
piecewise-linear scalar map with a single discontinuity - nowadays known as
nested period adding structure - was completely studied analytically by N. N.
Leonov already 50 years ago. He used an elegant and very efficient recursive
technique, which allows the analytical calculation of the border-collision
bifurcation curves, causing the nested period adding structure to occur. In
this work, we have demonstrated that the application of Leonov's technique is
not resticted to that particular bifurcation structure. On the contrary, the
presented map replacement approach, which is an extension of Leonov's
technique, allows the analytical calculation of border-collision bifurcation
curves for periodic orbits with high periods and complex symbolic sequences
using appropriate composite maps and the bifurcation curves for periodic orbits
with much lower periods.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2010-17&engl=0}
}
@article {ART-2010-13,
author = {Viktor Avrutin and Enric Fossas and Albert Granados and Michael Schanz},
title = {{Virtual orbits and two-parameter bifurcation analysis in a ZAD-controlled buck converter}},
journal = {Zeitschrift: Nonlinear Dynamics},
editor = {Springer-Verlag},
publisher = {Online},
pages = {1--15},
type = {Artikel in Zeitschrift},
month = {August},
year = {2010},
doi = {10.1007/s11071-010-9782-7},
keywords = {power electronics; zero average dynamics (ZAD) control; bifurcations; non-smooth systems; bifurcations; virtual orbits},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering},
contact = {Albert.Granados@ipvs.uni-stuttgart.de Viktor.Avrutin@ipvs.uni-stuttgart.de Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {Based on a recently obtained Lemma about periodic orbits in linear systems with
a piecewise-linear non-autonomous periodic control, we describe analytically
the bifurcation structures in a ZAD-controlled buck converter. This analytical
description shows that the period doubling bifurcation in this system may be
both subcritical or supercritical. Considering virtual orbits we show how a
saddle-node bifurcation becomes feasible and how it is destroyed at a new
codimension-2 bifurcation point, where the subcritical period doubling
bifurcation becomes supercritical. We also show that this phenomenon does not
take place when the error surface in the ZAD conditions piecewise-linear
defined.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2010-13&engl=0}
}
@article {ART-2010-05,
author = {Viktor Avrutin and Michael Schanz and Laura Gardini},
title = {{On a special type of border-collision bifurcations occurring at infinity}},
journal = {Physica D},
publisher = {Elsevier},
volume = {239},
number = {13},
pages = {1083--1094},
type = {Artikel in Zeitschrift},
month = {Juli},
year = {2010},
doi = {10.1016/j.physd.2010.02.015},
keywords = {Border-collision bifurcations; Piecewise-smooth maps; Piecewise-linear maps},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering,
G.2 Discrete Mathematics},
contact = { Michael.Schanz@informatik.uni-stuttgart.deViktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In piecewise-smooth dynamical systems, the regions of existence of a periodic
orbit are typically parameter sub-spaces confined by border-collision
bifurcations of this orbit. We demonstrate that additionally to the usual
border-collision bifurcations occurring at finite points in the state space
there exist also border-collision bifurcations occurring at infinity.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2010-05&engl=0}
}
@article {ART-2010-04,
author = {Viktor Avrutin and Partha Sharathi Dutta and Michael Schanz and Banerjee Soumitro},
title = {{Influence of a square-root singularity on the behaviour of piecewise smooth maps}},
journal = {Nonlinearity},
publisher = {IOP Science},
volume = {23},
number = {2},
pages = {445--463},
type = {Artikel in Zeitschrift},
month = {Februar},
year = {2010},
doi = {10.1088/0951-7715/23/2/012},
keywords = {Border-collision bifurcations; Piecewise-smooth maps},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering,
G.2 Discrete Mathematics},
ee = {http://iopscience.iop.org/0951-7715/23/2/012},
contact = { Michael.Schanz@informatik.uni-stuttgart.deViktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {We consider a one-dimensional continuous piecewise smooth nonlinear map with
square-root singularity. For particular choice of the parameters, this map
represents the normal form of discrete-time representation of impact oscillator
near grazing bifurcation. Owing to the nonlinearity, the map exhibits smooth
and nonsmooth bifurcations very closely related to each other. Our main aim is
to study how the nonlinearity influences the known results of nonsmooth
bifurcations and the interaction between smooth and nonsmooth bifurcations
considering the whole parameter space. We also explain the organizing source of
several atypical bifurcation phenomena using the concept of multi-parametric
bifurcation.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2010-04&engl=0}
}
@article {ART-2009-01,
author = {Viktor Avrutin and Bernd Eckstein and Michael Schanz},
title = {{The bandcount increment scenario. III. Deformed structures}},
journal = {Proceedings of the Royal Society A},
publisher = {Royal Society Publishing},
volume = {465},
number = {2101},
pages = {41--57},
type = {Artikel in Zeitschrift},
month = {Januar},
year = {2009},
doi = {10.1098/rspa.2008.0229},
keywords = {multi-band chaotic attractors; discontinuous maps; bandcount increment; bandcount adding; bandcount doubling},
language = {Englisch},
cr-category = {G.1.0 Numerical Analysis General,
J.2 Physical Sciences and Engineering},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {Bifurcation structures in two-dimensional parameter spaces formed by chaotic
attractors alone are still far away from being understood completely. In a
series of three papers, we investigate the chaotic domain without periodic
inclusions for a map, which is considered by many authors as some kind of
one-dimensional canonical form for discontinuous maps. In part I, the basic
structures in the chaotic region are explained by the bandcount increment
scenario. In part II, the fine self-similar sub-structures nested into the
bandcount increment scenario are explained by the bandcount adding and
bandcount doubling scenarios, nested into each other ad infinitum. Hereby we
fixed in both previous parts one of the parameters to a non-generic value and
studied the remaining two-dimensional parameter sub-space. In this part III
finally we investigate the structures under variation of this third parameter.
Remarkably, this step is most important with respect to practical applications,
since it can not be expected, that they operate exactly at this non-generic
value.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2009-01&engl=0}
}
@article {ART-2008-05,
author = {Viktor Avrutin and Bernd Eckstein and Michael Schanz},
title = {{The bandcount increment scenario. II. Interior structures}},
journal = {Proceedings of the Royal Society A},
publisher = {Royal Society Publishing},
volume = {464},
number = {2097},
pages = {2247--2263},
type = {Artikel in Zeitschrift},
month = {September},
year = {2008},
doi = {10.1098/rspa.2007.0299},
keywords = {multi-band chaotic attractors; discontinuous maps; bandcount increment; bandcount adding; bandcount doubling},
language = {Englisch},
cr-category = {G.1.0 Numerical Analysis General,
J.2 Physical Sciences and Engineering},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {Bifurcation structures in the two-dimensional parameter spaces formed by
chaotic attractors alone are still far away from being understood completely.
In a series of three papers, we investigate the chaotic domain without periodic
inclusions for a map, which is considered by many authors as some kind of
one-dimensional canonical form for discontinuous maps. In this second part, we
investigate fine substructures nested into the basic structures reported and
explained in part I. It is demonstrated that the overall structure of the
chaotic domain is caused by a complex interaction of bandcount increment,
bandcount adding and bandcount doubling structures, whereby some of them are
nested into each other ad infinitum leading to self-similar structures in the
parameter space.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2008-05&engl=0}
}
@article {ART-2008-04,
author = {Viktor Avrutin and Bernd Eckstein and Michael Schanz},
title = {{The bandcount increment scenario. I. Basic structures}},
journal = {Proceedings of the Royal Society A},
publisher = {Royal Society Publishing},
volume = {464},
number = {2095},
pages = {1867--1883},
type = {Artikel in Zeitschrift},
month = {Juli},
year = {2008},
doi = {10.1098/rspa.2007.0226},
keywords = {multi-band chaotic attractors; discontinuous maps; bandcount increment; bandcount adding; bandcount doubling},
language = {Englisch},
cr-category = {G.1.0 Numerical Analysis General,
J.2 Physical Sciences and Engineering},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {Bifurcation structures in 2D parameter spaces formed by chaotic attractors only
are still far away from being understood completely. In a series of three
papers we investigate the chaotic domain without periodic inclusions for a map
which is considered by many authors as some kind of 1D canonical form for
discontinuous maps. In the first part we report a novel bifurcation scenario
formed by crises bifurcations which includes multi-band chaotic attractors with
arbitrary high bandcounts and which determines the basic structure of the
chaotic domain.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2008-04&engl=0}
}
@article {ART-2008-02,
author = {Viktor Avrutin and Michael Schanz},
title = {{On the fully developed bandcount adding scenario}},
journal = {Nonlinearity},
publisher = {IOP Publishing},
volume = {21},
pages = {1077--1103},
type = {Artikel in Zeitschrift},
month = {April},
year = {2008},
doi = {10.1088/0951-7715/21/5/010},
keywords = {robust chaos, bandcount adding, crises bifurcations, piecewise linear discontinuous maps},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this paper we report a new bifurcation phenomenon induced by interior
crises, which explains the structure of multi-band chaotic attractors in the
case of a piecewise-linear discontinuous map. This phenomenon, denoted as a
fully developed bandcount adding scenario, leads to a self-similar structure of
the chaotic region in parameter space.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2008-02&engl=0}
}
@article {ART-2007-04,
author = {Viktor Avrutin and Michael Schanz and Soumitro Banerjee},
title = {{Codimension-3 bifurcations: Explanation of the complex 1-, 2- and 3D bifurcation structures in nonsmooth maps}},
journal = {Physical Review E},
publisher = {American Physical Society (APS)},
volume = {75},
number = {6},
pages = {1--7},
type = {Artikel in Zeitschrift},
month = {Juni},
year = {2007},
doi = {10.1103/PhysRevE.75.066205},
keywords = {discontinuity induced bifurcations; big bang bifurcations; period adding; period increment},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering},
ee = {http://link.aps.org/abstract/PRE/v75/e066205},
contact = {Viktor.Avrutin@informatik.uni-stuttgart.de Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {Many physical and engineerings systems exhibit cascades of periodic attractors
arranged in period increment and period adding sequences as a parameter is
varied. Such systems have been found to yield piecewise smooth maps, and in
some cases the obtained map is discontinuous. By investigating the normal form
of such maps, we have detected a new type of codimension-3 bifurcation which
serves as the organizing center of periodic and aperiodic dynamics in the
parameter space. The results will help in understanding the occurrence and
structure of such cascades observed in many nonsmooth systems in science and
engineering.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2007-04&engl=0}
}
@article {ART-2007-03,
author = {Viktor Avrutin and Bernd Eckstein and Michael Schanz},
title = {{On detection of multi-band chaotic attractors}},
journal = {Proceedings of the Royal Society A},
publisher = {The Royal Society},
volume = {463},
number = {2081},
pages = {1339--1358},
type = {Artikel in Zeitschrift},
month = {M{\"a}rz},
year = {2007},
doi = {10.1098/rspa.2007.1826},
keywords = {multi-band chaotic attractors; discontinuous maps; bandcount adding},
language = {Englisch},
cr-category = {G.1.0 Numerical Analysis General,
G.4 Mathematical Software,
J.2 Physical Sciences and Engineering},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work we present two numerical methods for the detection of the number
of bands of a multi-band chaotic attractor. The first method is more efficient
but can be applied only for dynamical systems with a continuous system
function, whereas the second one is applicable for dynamical systems with a
discontinuous system function as well. Using the developed methods, we
investigate a 1D piecewise-linear map and report for both cases of a continuous
and a discontinuous system function some new bifurcation scenarios involving
multi-band chaotic attractors.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2007-03&engl=0}
}
@article {ART-2006-09,
author = {Viktor Avrutin and Michael Schanz and Soumitro Banerjee},
title = {{Multi-parametric Bifurcations in a piecewise-linear discontinuous Map}},
journal = {Nonlinearity},
publisher = {IoP The Institute of Physics Publishing},
volume = {19},
pages = {1875--1906},
type = {Artikel in Zeitschrift},
month = {M{\"a}rz},
year = {2006},
doi = {10.1088/0951-7715/19/8/007},
keywords = {codimension-3; non-smooth dynamical systems; period adding; period increment},
language = {Englisch},
cr-category = {G.1.0 Numerical Analysis General,
J.2 Physical Sciences and Engineering},
contact = {Michael.Schanz@informatik.uni-stuttgart.de Viktor.Avrutin@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this paper a one-dimensional piecewise linear map with discontinuous system
function is investigated. This map actually represents the normal form of the
discrete-time representation of many practical systems in the neighbourhood of
the point of discontinuity. In the 3D parameter space of this system we detect
an infinite number of co-dimension one bifurcation planes, which meet along an
infinite number of co-dimension two bifurcation curves. Furthermore, these
curves meet at a few co-dimension three bifurcation points. Therefore, the
investigation of the complete structure of the 3D parameter space can be
reduced to the investigation of these co-dimension three bifurcations, which
turn out to be of a generic type. Tracking the influence of these bifurcations,
we explain a broad spectrum of bifurcation scenarios (like period increment and
period adding) which are observed under variation of one control parameter.
Additionally, the bifurcation structures which are induced by so-called big
bang bifurcations and can be observed by variation of two control parameters
can be explained.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2006-09&engl=0}
}
@article {ART-2006-02,
author = {Viktor Avrutin and Michael Schanz},
title = {{On multi-parametric Bifurcations in a scalar piecewise-linear Map}},
journal = {Nonlinearity},
publisher = {IoP The Institute of Physics Publishing},
volume = {19},
pages = {531--552},
type = {Artikel in Zeitschrift},
month = {M{\"a}rz},
year = {2006},
doi = {10.1088/0951-7715/19/3/001},
keywords = {codimension-3; non-smooth dynamical systems; period adding; period increment},
language = {Englisch},
cr-category = {G.1.0 Numerical Analysis General,
J.2 Physical Sciences and Engineering},
contact = {Viktor.Avrutin@informatik.uni-stuttgart.de, Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work a one-dimensional piecewise-linear map is considered. The areas in
the parameter space corresponding to specific periodic orbits are determined.
Based on these results it is shown that the structure of the 2D and 3D
parameter spaces can be simply described using the concept of multi-parametric
bifurcations. It is demonstrated that an infinite number of two-parametric
bifurcation lines starts at the origin of the 3D parameter space. Along each of
these lines an infinite number of bifurcation planes starts, whereas the origin
represents a three-parametric bifurcation.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2006-02&engl=0}
}
@article {ART-2005-04,
author = {Viktor Avrutin and Michael Schanz},
title = {{Period-doubling Scenario without Flip Bifurcations in a one-dimensional Map}},
journal = {International Journal of Bifurcation and Chaos},
publisher = {World Scientific Publishing Company},
volume = {15},
number = {4},
pages = {1267--1284},
type = {Artikel in Zeitschrift},
month = {April},
year = {2005},
doi = {10.1142/S0218127405012752},
keywords = {Period-doubling; border collision; piecewise-smooth vector field; kneading orbits},
language = {Englisch},
cr-category = {G.1.10 Numerical Analysis Applications,
J.2 Physical Sciences and Engineering},
contact = {Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {In this work a one-dimensional piecewise-smooth dynamical system, representing
a Poincar{\'e} return map for dynamical systems of the Lorenz type, is
investigated. The system shows a bifurcation scenario similar to the classical
period-doubling one, but which is influenced by so-called border collision
phenomena and denoted as border collision period-doubling bifurcation scenario.
This scenario is formed by a sequence of pairs of bifurcations, whereby each
pair consists of a border collision bifurcation and a pitchfork bifurcation.
The mechanism leading to this scenario and its characteristic properties, like
symmetry-breaking and symmetry-recovering as well as emergence of coexisting
attractors, are investigated.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2005-04&engl=0}
}
@article {ART-2003-12,
author = {Michael Schanz and Axel Pelster},
title = {{Synergetic System Analysis for the Delay-induced Hopf Bifurcation in the Wright Equation}},
journal = {SIAM Journal on Applied Dynamical Systems},
publisher = {SIAM Journals Online},
volume = {2},
pages = {277--296},
type = {Artikel in Zeitschrift},
month = {Januar},
year = {2003},
doi = {10.1137/S1111111102412802},
keywords = {Delay-induced Hopf Bifurcation, Wright equation},
language = {Englisch},
cr-category = {G.1.10 Numerical Analysis Applications},
contact = {Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {We apply the synergetic elimination procedure for the stable modes in nonlinear
delay systems close to a dynamical instability and derive the normal form for
the delay-induced Hopf bifurcation in the Wright equation. The resulting
periodic orbit is confirmed by numerical simulations.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2003-12&engl=0}
}
@article {ART-2003-11,
author = {Axel Pelster and Hagen Kleinert and Michael Schanz},
title = {{High-order variational Calculation for the Frequency of Time-periodic Solutions}},
journal = {Physical Review E},
editor = {The American Physical Society},
publisher = {Thomson ISI},
volume = {67, 016604},
pages = {1--6},
type = {Artikel in Zeitschrift},
month = {Januar},
year = {2003},
doi = {10.1103/PhysRevE.67.016604},
keywords = {variational techniques; nonlinear dynamical systems; perturbation theory},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering,
G.1.2 Numerical Analysis Approximation},
ee = {http://link.aps.org/abstract/PRE/v67/e016604},
contact = {Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {We develop a convergent variational perturbation theory for the frequency of
time-periodic solutions of nonlinear dynamical systems. The power of the theory
is illustrated by applying it to the Duffing oscillator.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2003-11&engl=0}
}
@article {ART-2003-10,
author = {Michael Schanz and Axel Pelster},
title = {{Analytical and numerical Investigations of the Phase-locked Loop with Time Delay}},
journal = {Physical Review E},
editor = {The American Physical Society},
publisher = {Thomson ISI},
volume = {67, 056205},
pages = {1--8},
type = {Artikel in Zeitschrift},
month = {Mai},
year = {2003},
doi = {10.1103/PhysRevE.67.056205},
keywords = {low-dimensional chaos; order parameter; bifurcation theory; normal form},
language = {Englisch},
cr-category = {J.2 Physical Sciences and Engineering,
G.1.9 Integral Functions},
ee = {http://link.aps.org/abstract/PRE/v67/e056205},
contact = {Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {We derive the normal form for the delay-induced Hopf bifurcation in the
first-order phase-locked loop with time delay by the multiple scaling method.
The resulting periodic orbit is confirmed by numerical simulations. Further
detailed numerical investigations demonstrate exemplarily that this system
reveals a rich dynamical behavior. With phase portraits, Fourier analysis, and
Lyapunov spectra it is possible to analyze the scaling properties of the
control parameter in the period-doubling scenario, both qualitatively and
quantitatively. Within the numerical accuracy there is evidence that the
scaling constant of the time-delayed phase-locked loop coincides with the
Feigenbaum constant deltaapproximate to4.669 in one-dimensional discrete
systems.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2003-10&engl=0}
}
@proceedings {PROC-2005-01,
editor = {Paul Levi and Michael Schanz},
title = {{Autonome Mobile Systeme 2005}},
address = {Berlin, Heidelberg, New York},
publisher = {Springer-Verlag},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Elektrotechnik und Informationstechnik, Germany},
series = {Informatik Aktuell},
pages = {332},
type = {Tagungsband},
month = {Dezember},
year = {2005},
isbn = {978-3-540-30291-9},
keywords = {Autonome Mobile Systeme},
language = {Deutsch},
cr-category = {I.2.9 Robotics,
I.2.10 Vision and Scene Understanding,
I.2.11 Distributed Artificial Intelligence,
I.4.7 Image Processing and Computer Vision Feature Measurement,
I.4.8 Image Processing and Computer Vision Scene Analysis,
I.5.4 Pattern Recognition Applications,
J.7 Computers in Other Systems},
contact = {Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte Systeme, Bildverstehen},
abstract = {Die Fachgespr{\"a}che Autonome Mobile Systeme (AMS) repr{\"a}sentieren ein Forum, in
dem die neuesten Entwicklungen auf dem Gebiet wissenschaftlicher und
industrieller autonomer Robotersysteme, sowie verwandter Gebiete vorgestellt
werden.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=PROC-2005-01&engl=0}
}
@proceedings {PROC-2001-01,
editor = {Paul Levi and Michael Schanz},
title = {{Autonome Mobile Systeme 2001}},
address = {Berlin, Heidelberg, New York},
publisher = {Springer-Verlag},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Germany},
series = {Informatik Aktuell},
pages = {193},
type = {Tagungsband},
month = {September},
year = {2001},
isbn = {3-540-42552-7},
keywords = {Autonome Mobile Systeme},
language = {Deutsch},
cr-category = {I.2.9 Robotics,
I.2.10 Vision and Scene Understanding,
I.2.11 Distributed Artificial Intelligence,
I.4.8 Image Processing and Computer Vision Scene Analysis,
I.4.9 Image Processing and Computer Vision Applications,
I.5.4 Pattern Recognition Applications},
contact = {Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte H{\"o}chstleistungsrechner, Bildverstehen},
abstract = {Die Fachgespr{\"a}che Autonome Mobile Systeme (AMS) repr{\"a}sentieren ein Forum, in
dem die neuesten Entwicklungen auf dem Gebiet wissenschaftlicher und
industrieller autonomer Robotersysteme, sowie verwandter Gebiete vorgestellt
werden.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=PROC-2001-01&engl=0}
}
@proceedings {PROC-1998-01,
editor = {Paul Levi and Michael Schanz},
title = {{Mustererkennung 1998}},
address = {Berlin, Heidelberg, New York},
publisher = {Springer-Verlag},
institution = {Universit{\"a}t Stuttgart, Fakult{\"a}t Informatik, Germany},
series = {Informatik Aktuell},
pages = {590},
type = {Tagungsband},
month = {September},
year = {1998},
isbn = {3-540-64935-2},
keywords = {Mustererkennung},
language = {Deutsch},
cr-category = {A.0 General Literature, General,
I.2 Artificial Intelligence,
I.2.7 Natural Language Processing,
I.2.10 Vision and Scene Understanding,
I.2.11 Distributed Artificial Intelligence,
I.3 Computer Graphics,
I.4 Image Processing and Computer Vision,
J.3 Life and Medical Sciences},
contact = {Michael.Schanz@informatik.uni-stuttgart.de},
department = {Universit{\"a}t Stuttgart, Institut f{\"u}r Parallele und Verteilte H{\"o}chstleistungsrechner, Bildverstehen},
abstract = {Die Deutsche Arbeitsgemeinschaft f{\"u}r Mustererkennung (DAGM) veranstaltet seit
1978 j{\"a}hrlich ein wissenschaftliches Symposium mit dem Ziel,
Aufgabenstellungen, Denkweisen und Forschungsergebnisse aus den Gebieten der
Mustererkennung vorzustellen, den Erfahrungs- und Ideenaustausch zwischen
Fachleuten anzuregen und den Nachwuchs zu f{\"o}rdern.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=PROC-1998-01&engl=0}
}