Applied Nonlinear Dynamics (etit614)
Angewandte nichtlineare Dynamik / Applied Nonlinear Dynamics
VUE; 3 SWS; ECTSPoints: 4
Lecturer: Dr. Alexander Schaum
Overview
 Linear and nonlinear dynamical systems
 Qualitative behavior of vector fields
 Local and nonlocal bifurcations
 Introduction to discretetime 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:
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.
 Exercise 1 > solution and python code
 Exercise 2 > solution
 Exercise 3 > solution (code for ex. 3.3)
 Exercise 4 > solution (maxima code)
 Exercise 5 > solution
 Exercise 6 > solution
 Exercise 7 > solution
 Exercise 8 > solution
 Exercise 9 > solution
 Exercise 10 > solution
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.
ComputerAlgebraSystem Maxima
 Download Maxima (console) or wxMaxima (GUI) at Sourceforge

Introduction to Maxima using the GUI wxMaxima
Octave

Download Octave
Note that you will need to install the odepkg and when needed load it using: pkg load odepkg
Python2
 Download 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, AddisonWesley
[6] S. Wiggins: Introduction to Applied Nonlinear Systems and Chaos, Springer
[7] S. Sastry: Nonlinear Systems: Analysis, Stability, and Control, Springer.