Course syllabus

Olinjära dynamiska system
Nonlinear Dynamical Systems

FMAN15, 7,5 credits, A (Second Cycle)

Valid for: 2016/17
Decided by: Education Board B
Date of Decision: 2016-03-29

General Information

Elective for: D4, F4, F4-bs, F4-bm, Pi4-bs, Pi4-ssr, Pi4-biek
Language of instruction: The course will be given in English


To give knowledge of and familiarity with concepts and methods from the theory of dynamical systems which are important in applications within almost all subjects in science and technology. In addition, the course should develop the student's general ability to assimilate and communicate mathematical theory, to express problems from science and technology in mathematical terms and to solve problems using the theory of dynamical systems.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must


Dynamical systems in discrete and continuous time. The fixed point theorem and Picard's theorem on the existence and uniqueness of solutions to ordinary differential equations. Phase space analysis and Poincaré's geometrical methods. Local stability theory (Liapunov's method and Hartman-Grobman's theorem). The central manifold theorem. Basic local bifurcation theory. Global bifurcations and transition to chaos. Chaotic and strange attractors (dynamics, combinatorial description).

Examination details

Grading scale: TH
Assessment: Written and/or oral test, to be decided by the examiner. Some written assignments to be completed before the exam.


Required prior knowledge: FMAF05 Systems and Transforms, or similar.
The number of participants is limited to: No
The course overlaps following course/s: FMA140, FMA141

Reading list

Contact and other information

Course coordinator: Anders Holst,
Teacher: Mario Natiello,
Teacher: Jörg Schmeling,
Course homepage: