Applied Nonlinear Dynamics (etit-614)

Angewandte nichtlineare Dynamik / Applied Nonlinear Dynamics

See  UnivIS (lecture ID 080152) and UnivIS (lecture ID 080184)

V-UE; 3 SWS; ECTS-Points: 4

Lecturer: Dr. Alexander Schaum

 

Overview

The course gives an introduction to the qualitative analysis of nonlinear differential and difference equations, in particular on bifurcations in one, two and higher-dimensional nonlinear systems. The lecture addresses the following topics:
 
  • Linear and nonlinear dynamical systems
  • Qualitative behavior of vector fields
  • Local and non-local bifurcations
  • Introduction to discrete-time nonlinear systems
  • Introduction to chaotic systems
  • Aspects of nonlinear dynamics in control systems design
     

Dates

Important information for summer term 2020
  • Unless not announced otherwise due to the Corona virus crisis the course will take place as a digital course.
  • Students should register until April 6th, 2020 using the OLAT resource of the course.
  • A preliminary online meeting will be announced on April 6th, 2020 

 

Downloads

Course material (lecture notes and exercises) will be provided during the course after the start of the semester.

The exercises will be accompanied by simulation and numerical evaluation tasks using open-source software like Maxima, Octave and Python.

Computer-Algebra-System Maxima

Octave

        Note that you will need to install the odepkg and when needed load it using:     pkg load odepkg

Python2


 

Literature

[1] S. Strogatz: Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry, and engineering, Perseus Books
[2] L. Perko: Differential Equations and Dynamical Systems, Springer
[3] J. Hale, H. Kocak: Dynamics and Bifurcations, Springer
[4] S. Lynch: Dynamical Systems with Applications using Mathematica, Birkhäuser
[5] R. Abraham: C. Shaw: Dynamics: The Geometry of Behavior, Addison-Wesley
[6] S. Wiggins: Introduction to Applied Nonlinear Systems and Chaos, Springer
[7] S. Sastry: Nonlinear Systems: Analysis, Stability, and Control, Springer.

Research