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
  • Aspects of nonlinear dynamics in control systems design
     
 

Dates

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

 

Downloads

 

Lecture Notes

 

Parts:

 

 

 

Exercises

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

 

The complete lecture notes from summer term 2015 can be downloaded here: LN_SS15.pdf

 

Some of the exercises will require numerical analysis using the computer-algebra systems Maxima and  Octave or MatLab.

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