Students will successfully handle various tools from the Qualitative Theory of Dynamical Systems in order to understand models describing time-varying problems.

Lecture at blackboard

A Dynamical System describes the time-dependence of a given process. Analyzing the dynamical system helps to "predict the future" of such processes. Many applications arise naturally from biology (population dynamics, epidemiology, neural networks etc.),  physics (e.g. position (and velocity) of a particle/spacecraft/planet etc.), chemistry (e.g. reaction kinetics), economics (e.g. macroeconomic-, monetary- and business models) and weather forecast.Basics: Invariant and minimal sets, limit sets, attractorsDiscrete dynamical systems: Linear dynamical systems, linearization, invariance principle, Hartman-Grobman theoremContinuous dynamical systems: Lyapunov functions, planar equations (planar linear equations, Poincaré-Bendixson theory, closed orbits), stability

Analysis 1-3, Linear Algebra 1-2, Ordinary differential equations

Lecture notesH. Amann: Ordinary Differential Equations: An Introduction to Nonlinear Analysis, Studies in Mathematics 13, de Gruyter, 1990J.K. Hale, H. Koçak: Dynamics and Bifurcations, Springer, Berlin etc., 1991R. Clark Robinson: An Introduction to Dynamical Systems: Continuous and Discrete (2nd ed), Pure and Applied Undergraduate Texts 19, AMS, Providence RI, 2012

Written examDates will be discussed during the first lecture.

Contents of the course

50% of the obtained points are sufficient to pass the exam