PhD Course: Piecewise smooth dynamical systems
May 5-9, 2014
Technical University of Denmark, Lyngby (Copenhagen), Denmark
A course given
Hogan, Bristol University, currently Otto Mønsted Guest Professor
at the Technical University of Denmark.
Course description Mechanical systems with impacts and
friction, biological systems with thresholds and social systems with
limiting factors are all examples of piecewise smooth systems. To the
mathematician, they are fascinating and challenging, since they call
into question the very notion of the solution to a differential
equation. In applications, they are vital to the understanding of
control systems, gene regulation and all sorts of mechanical
systems. In fact, piecewise smooth system contain not only classical
nonlinear behavior such as bifurcations and chaos, but also unique
dynamics such as sliding and period adding bifurcations that are seen
in applications. Yet, despite their ubiquity, surprisingly little is
known about the dynamics of these systems.
In this course, we shall consider many topics, which will give a
flavour of the large range of unsolved problems in this field. We will
start with the basics, covering piecewise smooth maps and flows, then
look at some modeling and mathematical challenges, consider numerical
methods and smoothing and bring students right up to date with the
classification of sliding bifurcations and the use of Melnikov
methods. Students should have a basic background in dynamics (for
example, a familiarity with topics in Strogatz's book Nonlinear
Dynamics and Chaos would be useful), and may be interested in
Section, Department of
Applied Mathematics and Computer
Science, Technical University
of Denmark. mobr (at) dtu.dk
The course is designed for Ph.D.-students and final-year graduate students being familiar with the basic concepts of dynamical systems.
The course gives 5 ECTS corresponding to approximately 130 hours in total, which includes work during the course period at DTU (lectures, exercises, and discussions) as well as project work after the course week.
Course material will be provided to the participants.
All lectures will be given in English.
To pass the course, active participation in all activities is required; this includes discussions, exercises, and project work. A project report must be handed on the 1st of June 2014. The course is passed/not passed. ECTS points: 5.
Anne Mette Eltzholtz Larsen, Department of Applied Mathematics and Compute Science, Technical University of Denmark, Building 303B, DK-2800 Kgs. Lyngby, Denmark. Phone: (+45) 4525 5246 , E-mail: amel (at) dtu.dk.
There is a no registration fee for students enrolled at universities and public research institutions.
Applicants should submit a request for registration by e-mail
to amel (at) dtu.dk. Registration is on a
first-come-first-served basis. Max 25 participants.
Participants are requested to arrange their own
accommodation. Suggestions will appear shortly.
This course is supported by the PhD-school ITMAN and The Otto Mønsted
Last updated: 4 March 2014