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Nonlinear Dynamics

Module MA3082

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2012

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

available module versions
WS 2017/8SS 2012WS 2011/2

Basic Information

MA3082 is a semester module in English language at Bachelor’s level which is offered in winter semester.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


Elements of phase space analysis: equilibria, periodic orbits, concepts of stability, invariant sets, local vs global dynamics. Linearization. Poincaré-Bendixon theory. Steady state bifurcations: Fold, Hopf. Perturbation theory, asymptotics, averaging. Examples of chaotic dynamics: one-dimensional maps, three-dimensional flows; basics of symbolic dynamics. Applications (from engineering, natural sciences, etc.)

Learning Outcome

Nach dem erfolgreichen Abschluss des Moduls sind die Studierenden in der Lage, die grundlegende mathematische Theorie endlich-dimensionaler kontinuierlicher sowie diskreter dynamischer Systeme zu verstehen und deren analytische Behandlung zu beherrschen. Sie sind vertraut mit der Nutzung relevanter Software.


MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2, MA2004 Vector Analysis, MA2005 Ordinary Differential Equations

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.




Wiggins, Stephen: Introduction to Applied Nonlinear Dynamical Systems and Chaos; Springer-Verlag, New York 1990.
Chow, S.-N./Hale, J. K.: Methods of Bifurcation Theory; Springer-Verlag, New York 1995.

Module Exam

Description of exams and course work

The module examination is based on a written exam (60 minutes). For the exam students have to know basic concepts and methods of the mathematical theory of nonlinear dynamical systems and can apply them adequately and with mathematical precision to problems of this field.

Exam Repetition

The exam may be repeated at the end of the semester.

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