Applied Nonlinear Dynamics (etit-614)


Angewandte nichtlineare Dynamik / Applied Nonlinear Dynamics


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

Lecturer: Dr. Alexander Schaum



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


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




Lecture Notes


The complete lecture notes of summer term 2018 can be downloaded here.




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 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 computer-algebra systems Maxima and  Octave or MatLab.

Computer-Algebra-System Maxima



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




[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.