WS 2015 SS 2015
WS 2014
WS 2013 SS 2014
Department of Physics
open chemistry
KVL / Klausuren / MAP 1st HS: 13.10  2nd HS: 08.12  sem.br.: 16.02  begin SS: 13.04

4020145155 Dynamical systems: nonlinear Dynamics  VVZ 

VL
Fri 13-15
weekly NEW 14 1'11 (30) Michael Zaks
UE
Fri 11-13
14-day NEW 14 1'13 (21) Michael Zaks

Digital- & Präsenz-basierter Kurs

Aims
The course is concepted as an introduction into the
problematics, ideas and methods of the modern nonlinear dynamics. The underlying mathematical formalism will be illustrated by examples from applications: fluid dynamics, neuroscience, populational dynamics. The students will learn how to determine the stability of steady and oscillatory states, and how to deal with chaotic behavior. The acquired knowledge can be later applied to various fields of the modern natural science.
Requirements
Vordiplom in Physik; Bachelorarbeit in der Physik
Structure / topics / contents
* Dynamical systems: discrete and continuous, dissipative and Hamiltonian.
* Various definitions of stability and their physical meaning.
* Local bifurcations of equilibria and periodic solutions. Poincare-mapping. Global bifurcations.
* Bifurcational scenarios and universal transitions to chaos.
* Chaotic attractors and their fractal properties.
* Lyapunov exponents
* Introduction into the KAM-theory and the Hamiltonian chaos.
* Examples from fluid mechanics, population models
(ecology), neurodynamics.
Assigned modules
P23.3.1 P23.3
Amount, credit points; Exam / major course assessment
3 SWS, 5 SP/ECTS (Arbeitsanteil im Modul für diese Lehrveranstaltung, nicht verbindlich)
Written exam
Other
ACHTUNG: Diese Veranstaltung findet wegen Krankheit nicht statt,
Empfehlung: 40569 Komplexe Netzwerke - Theorie und Anwendungen
Contact
PD Dr. Michael Zaks (3'410)
Literature
Argyris, Faust, Haase, Friedrich. Die Erforschung des Chaos. Springer
Glendinning. Stability, Instability and Chaos. Cambridge University Press
Ott. Chaos in Dynamical Systems. Cambridge University Press
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