151-0532-00L  Nonlinear Dynamics and Chaos I

SemesterHerbstsemester 2016
DozierendeG. Haller, F. Kogelbauer
Periodizitätjährlich wiederkehrende Veranstaltung


KurzbeschreibungBasic facts about nonlinear systems; stability and near-equilibrium dynamics; bifurcations; dynamical systems on the plane; non-autonomous dynamical systems; chaotic dynamics.
LernzielThis course is intended for Masters and Ph.D. students in engineering sciences, physics and applied mathematics who are interested in the behavior of nonlinear dynamical systems. It offers an introduction to the qualitative study of nonlinear physical phenomena modeled by differential equations or discrete maps. We discuss applications in classical mechanics, electrical engineering, fluid mechanics, and biology. A more advanced Part II of this class is offered every other year.
Inhalt(1) Basic facts about nonlinear systems: Existence, uniqueness, and dependence on initial data.

(2) Near equilibrium dynamics: Linear and Lyapunov stability

(3) Bifurcations of equilibria: Center manifolds, normal forms, and elementary bifurcations

(4) Nonlinear dynamical systems on the plane: Phase plane techniques, limit sets, and limit cycles.

(5) Time-dependent dynamical systems: Floquet theory, Poincare maps, averaging methods, resonance
SkriptThe class lecture notes will be posted electronically after each lecture. Students should not rely on these but prepare their own notes during the lecture.
Voraussetzungen / Besonderes- Prerequisites: Analysis, linear algebra and a basic course in differential equations.

- Exam: two-hour written exam in English.

- Homework: A homework assignment will be due roughly every other week. Hints to solutions will be posted after the homework due dates.


Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte4 KP
PrüfendeG. Haller, F. Kogelbauer
Testat erforderlichNein
RepetitionDie Leistungskontrolle wird nur am Semesterende nach der Lerneinheit angeboten. Die Repetition ist nur nach erneuter Belegung möglich.
Zusatzinformation zum Prüfungsmodus- Written 120 minutes
- Written aids: Students can use the class lecture notes and a calculator during the written exam. No further material is allowed.


Es werden nur die öffentlichen Lernmaterialien aufgeführt.


151-0532-00 VNonlinear Dynamics and Chaos I2 Std.
Mi10-12HG D 7.1 »
G. Haller, F. Kogelbauer
151-0532-00 UNonlinear Dynamics and Chaos I2 Std.
Do16-18HG D 7.1 »
G. Haller, F. Kogelbauer


Keine zusätzlichen Belegungseinschränkungen vorhanden.

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