# Numerics of Dynamical Systems (MA 3333)

*Prof. Dr. Oliver Junge, Dipl.-Math. Alex Schreiber*

## 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 numercially. These are questions which are being treated in this lecture, tying in with MA 3082

*Nonlinear Dynamics*.

## Lecture

- Date: Tuesday, 12:15-13:45, MI 02.08.011
- Notes/Programs

## Tutorial

- Tutor: Alex Schreiber
- Date: Every second Tuesday:

2015-10-27, 2015-11-10, 2015-11-24, 2015-12-08, 2015-12-22,

2016-01-12, 2016-01-26 - 08:30-10:00, MI 02.08.020
- Please bring a laptop with MATLAB into the tutorial.

## Exams

- Date: The first exam took place on Monday, 2016-02-08, at 10:00-11:00 h. Place: 00.04.011, MI Hörsaal 2 (5604.EG.011).
- Date: The repetition exam took place on Tuesday, 2016-03-29, at 09:00-10:00 h. Place: 02.08.011, Seminarraum (M2/M3) (5608.02.011).
- Problems will be in English. You may write your solutions in German or English.
- Bring your valid studentCard and an official ID.
- The exam takes 60 minutes and spans the material of the lectures and exercises.
- As only auxiliary tool you may bring a a4 paper with (written/printed/copied...; two-sided) notes into the exam.
- Beyond that, you only need writing utensils. Draft paper will be distributed.
- Einsicht/Inspection/Copies of first exam: Wednesday, 2016-02-10, 14:00 @ Besprechungsraum ("Glaskasten") 02.10.022B.
- Einsicht/Inspection/Copies of repetition exam: Tuesday, 2016-03-29, 16:00 @ 02.08.057

## 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.