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

 

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

 





 
 

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