Einladung zum Vortrag im Kolloquium Technische Kybernetik

Discontinuity-induced phenomena - lost in parameter space?

Dr. rer. nat. Viktor Avrutin

Abt. Bildverstehen
Institut für Parallele und Verteilte Systeme
Universität Stuttgart

    Zeit: Dienstag · 7. 3. 2006 · 16:00 Uhr
    Ort: Seminarraum 3.241 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen

Abstract

Recently the behavior of piecewise smooth dynamical systems has received significant research attention because a large number of systems of practical interest are modeled by such systems. This includes power electronic circuits, systems involving relays, mechanical systems with impacts and stick-slip oscillations, cardiac dynamics, walking robots etc. As shown in several works, the behavior of these systems is strongly influenced by border-collision bifurcations. Remarkably, these bifurcations turned out to be important not only for piecewise smooth dynamical systems, but to be of a general interest. This is due to the fact that Poincare return maps of smooth dynamical systems, like for instance the well-known Lorenz system, are often discontinuous and demonstrate these bifurcations as well.
Meanwhile the one-parametric (co-dimension one) border-collision bifurcations are well investigated. However, when investigating one-parametric bifurcation scenarios in extended parameter intervals one observes often bifurcation sequences, which are very difficult to understand. Most unexpectedly, increasing the dimension of the considered parameter space, it is possible to obtain much better understandable bifurcation structures, caused by two- and three-parametric bifurcations. They serve as some kind of organizing centers in multi-dimensional parameter spaces and dominate their structure.
In the talk an introduction of those aspects of bifurcation theory will be given which are relevant for the above-mentioned topics. It will be shown how the investigation of a dynamical system under variation of one control parameter may lead to results which are very difficult to interpret. These results become well-understandable if one considers the corresponding structures in the two-dimensional parameter space, although an infinite number of bifurcation curves are involved. Additionally, some examples of three-parametric (co-dimension three) bifurcations will be presented.

Biographical Information

Dr. Viktor Avrutin received the B.Sc. from the the St. Petersburg State Polytechnical University (Russia), the M.Sc. and the Ph.D. from the University of Stuttgart (Germany). He is currently working at the Institute of Parallel and Distributed Systems (IPVS), University of Stuttgart.
Primary scientific interest: behavior of non-smooth dynamical systems Secondary scientific interest: development of software tools for investigation of dynamical systems (see http://www.AnT4669.de/). Primary non-scientific interest: origami