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)
Downloads
Lecture Notes
The complete lecture notes of summer term 2018 can be downloaded here.
 ss18_part1.pdf
 ss18_part2.pdf (update from April 25, 2018)
 ss18_part3.pdf
 ss18_part4.pdf
 ss18_part5.pdf
 ss18_part6.pdf
 ss18_part7.pdf
 ss18_part8.pdf
 For part9 see the complete notes
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 with solution and codes for 1.1 and 1.4
 Exercise 2 with solutions
 Exercise 3 with codes for 3.2 (Octave/Matlab) and 3.3/3.4 (wxmaxima)
 Exercise 4 with solution of 4.1b)
 Exercise 5 with solution
 Exercise 6 with solution
 Exercise 7 with solution
 Exercise 8 with solution
 Exercise 9 with solution
 Exercise 10 with solution (example mFiles for E10_1 and E10_4)
 Exercise 11 with solution
The complete lecture notes from summer term 2017 can be downloaded here: Complete Lecture notes from SS2017.
Some of the exercises will require numerical analysis using the computeralgebra systems Maxima and Octave or MatLab.
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.