# 312.101 (19W) Dynamical Systems 1, Exercises

## Wintersemester 2019/20

Anmeldefrist abgelaufen.

Erster Termin der LV
02.10.2019 17:00 - 18:00 , N.2.01
Nächster Termin:
11.12.2019 17:00 - 18:00 , N.2.01
Nächster gültiger Termin:
08.01.2020 17:00 - 18:00 , N.2.01

## Überblick

Lehrende/r
LV-Titel englisch
Dynamical Systems 1, Exercises
LV-Art
Übung (prüfungsimmanente LV )
Semesterstunde/n
1.0
ECTS-Anrechungspunkte
2.0
Anmeldungen
4 (25 max.)
Organisationseinheit
Unterrichtssprache
Englisch
mögliche Sprache/n der Leistungserbringung
Englisch
LV-Beginn
02.10.2019

Excercises

## Inhalt/e

A dynamical system describes the time-dependence of a given process. Analyzing the dynamical system helps to "predict the future" of the process. 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, attractors

Discrete dynamical systems: Linear dynamical systems, linearization, invariance principle

Continuous dynamical systems: Lyapunov functions, planar equations (planar linear equations, Poincaré-Bendixson theory, closed orbits), stability

## Literatur

See lecture notes.

Further literature:

H. Amann, Ordinary differential equations: An introduction to nonlinear analysis, de Gruyter, Berlin etc., 1990

R. Clarke Robinson, An introduction to dynamical systems - Continuous and discrete, AMS, Providence RI, 2012

## Prüfungsinformationen

### Prüfungsmethode/n

Written test; solving and handing in/ presenting assignments. We will agree on the details on the first week.

Exercises

### Beurteilungskriterien/-maßstäbe

50% of the overall points are sufficient to obtain a positive grade.

## Position im Curriculum

• Doktoratsprogramm Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (SKZ: ---, Version: 16W.1)
• Fach: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (Pflichtfach)
• Modeling-Analysis - Optimization of discrete, continuous and stochastic systems ( 0.0h XX / 0.0 ECTS)
• 312.101 Dynamical Systems 1, Exercises (1.0h UE / 2.0 ECTS)
• Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
• Fach: Applied Analysis (Wahlfach)
• 4.1 Dynamical Systems 1 ( 1.0h UE / 2.0 ECTS)
• 312.101 Dynamical Systems 1, Exercises (1.0h UE / 2.0 ECTS)
• Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
• Fach: Applied Mathematics (Wahlfach)
• Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
• 312.101 Dynamical Systems 1, Exercises (1.0h UE / 2.0 ECTS)
• Masterstudium Technische Mathematik (SKZ: 401, Version: 13W.1)
• Fach: Angewandte Analysis (Wahlfach)
• Dynamische Systeme 2 ( 3.0h VU / 6.0 ECTS)
• 312.101 Dynamical Systems 1, Exercises (1.0h UE / 2.0 ECTS)
• Doktoratsstudium Doktoratsstudium der Technischen Wissenschaften (SKZ: 786, Version: 12W.4)
• Fach: Studienleistungen gem. § 3 Abs. 2a des Curriculums (Pflichtfach)
• Studienleistungen gem. § 3 Abs. 2a des Curriculums ( 16.0h XX / 32.0 ECTS)
• 312.101 Dynamical Systems 1, Exercises (1.0h UE / 2.0 ECTS)

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