Applied Nonlinear Dynamics (etit-614)

 

Angewandte nichtlineare Dynamik / Applied Nonlinear Dynamics

 

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

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

 

Examination:

In order to find appropriate dates for the oral examination please contact the lecturer under alsc@tf.uni-kiel.de
The content for the exam will be based on parts I and III of the lecture notes (part II on discrete-time systems was not covered this semester)
The examination  can be carried out within the following intervals:
17.07 - 26.07.2019
12.08 - 30.08.2019
09.09 - 20.09.2019
For the possibility of taking the exam at the beginning of october please contact the lecturer.

 

Downloads

 

Lecture Notes

The lecture notes for summer term 2019 can be downloaded here

Slides: Introduction to chaos

 

Exercises

The exercises will take place with one week displacement, i.e. the exercise on the material of week n is discussed in week n+1.

 

The exercises will be accompanied by simulation and numerical evaluation tasks like Maxima, Octave and Python. A short introduction to the used tools will be provided in the exercise classes.

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