## Numerics of Dynamical Systems (MA3333)

Prof. Dr. Oliver Junge, Michael Kratzer

### Content

Dynamical Systems are mathematical models of systems which change their state with time. Typical examples are (certain) ordinary or partial differential equations. A basic question for a such system is of course to compute its temporal evolution, given a particular initial condition, i.e. to simulate the system.

Often, however, one is interested in the targeted computation of particular solutions, e.g. equilibrium points (i.e. states which do not change with time), periodic solutions or connecting orbits. In addition, many models from applications exhibit complicated dynamics. Here, the questions is how one can describe the dynamics of such systems over long time spans and how these descriptions can be reliably approximated numerically. These are questions which are being treated in this lecture, tying in with MA 3082 Nonlinear Dynamics.

### News

No lecture on Dec 6, 2016 and on Jan 17, 2017.

### Tutorial

• Time and Place: Every second Thursday, starting 2016-10-27, 8:30-10:00, MI 03.08.011
• Please bring a computer with MATLAB installed. We will use the GAIO toolbox , which can be downloaded from GitHub .

No. Discussion Problem Sheet Additional material
1 2016-10-27 Exercise1.pdf
3 2016-12-01 Exercise3.pdf attractor.m, Solutions to P3.1 and P3.2
2 2016-11-17 Exercise2.pdf Auxiliary functions, Solution to P2.2
5 2017-01-12 Exercise5.pdf Solution to P5.2
6 2017-01-26 Exercise6.pdf Solution to P6.2
4 2016-12-15 Exercise4.pdf unstable_manifold.m, Solution to P4.2
(No tutorial on 2017-02-09)

### Exam

• Time and Place: Tuesday, 2017-02-21, 11:00-12:00 in 00.04.011, MI Hörsaal 2 (5604.EG.011)
• The exam will be posed in English (questions can, however, be answered in either English or German).
• Please bring your valid student ID and an official ID (passport, Personalausweis or similar).
• You may bring one A4 sheet (written/printed/copied...; two-sided) of notes. No other tools or aids are allowed.
• You will be able to review your marked exam on Friday, 2017-02-24, 14:00-15:30 in MI 02.08.011.

### References

• Govaerts, W. J. F.: Numerical methods for bifurcations of dynamical equilibria, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000.
• Guckenheimer, J.; Holmes, P.: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer, New York, 1990.
• Kreuzer, E.: Numerische Untersuchung nichtlinearer dynamischer Systeme, Springer, Berlin, 1987.
• Stuart, A.M.; Humphries, A.R.: Dynamical systems and numerical analysis, Cambridge University Press, 1998.
• Parker, T.S.; Chua, L.O.: Practical numerical algorithms for chaotic systems, Springer, New York, 1989.
• Lasota, A.; Mackey, M.C.: Chaos, Fractals, and Noise, Springer, New York, 1994.