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
  • Aspects of nonlinear dynamics in control systems design



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

  • Preliminary program (updated May, 17)
  • Possible dates for exams:    August 8, 23-26,    September 9,12,16,19,20, 26-30,       October 3-13.


Lecture Notes



                                      ->  Solutions to selected problems: octave (requires odepkg), wxmaxima, pdf
                                      -> Solution to Problem 4.1 b): octave (requires odepkg), pdf
  • Exercise 5 - Nonlocal analysis I: Index theory, Lienard systems.
                                      -> Solution example to Problem 5.4: octave (requires odepkg)
  • Exercise 6 - Nonlocal analysis II: Criteria of Poincaré-Bendixson, Bendixson-Dulac, Lyapunov
  • Exercise 7 - Bifurcations I
  • Exercise 8 - Bifurcations II - Miniproject: Exothermic CSTR
  • Exercise 9 - Discrete-time systems I
                                      -> Octave programs: SolEx91.m, phase_portrait.m


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



        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.