4020225156 Dynamical systems: Nonlinear Dynamics
Digital- & Präsenz-basierter Kurs
- classroom language
- DE
- 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. Acquired knowledge can be later applied to various fields of the modern natural science.
- requirements
- BA in physics
- 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
-
P25.3.b
- amount, credit points; Exam / major course assessment
- 4 SWS, 6 SP/ECTS (Arbeitsanteil im Modul für diese Lehrveranstaltung, nicht verbindlich)
Oral exam
- contact
- PD Dr. Michael Zaks (Newtonstr. 15, Raum 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
- quod vide:
- http://people.physik.hu-berlin.de/~zaks/lehre.html
- Moodle link:
- http://moodle.hu-berlin.de/course/view.php?id=115296