Applied Nonlinear Dynamics (etit-614)
V-UE; 3 SWS; ECTS-Points: 4Lecturer: Dr. Alexander Schaum
- 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
- Preliminary program (updated May, 17)
- Possible dates for exams: August 8, 23-26, September 9,12,16,19,20, 26-30, October 3-13.
- Exercise 1 - Linear (time-invariant) systems
- Exercise 2 - Linear time-varying systems
- Exercise 3 - Nonlinear Dynamics I: Local analysis
- Exercise 4 - Nonlinear Dynamics II: Center manifold theory
-> Solution to Problem 4.1 b): octave (requires odepkg), pdf
-> Solution example to Problem 5.4: octave (requires odepkg)
- Exercise 5 - Nonlocal analysis I: Index theory, Lienard systems.
-> Octave programs: SolEx91.m, phase_portrait.m
- 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
- Exercise 10 - Discrete-time systems II
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.
Note that you will need to install the odepkg and when needed load it using: pkg load odepkg
 S. Strogatz: Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry, and engineering, Perseus Books
 L. Perko: Differential Equations and Dynamical Systems, Springer
 J. Hale, H. Kocak: Dynamics and Bifurcations, Springer
 S. Lynch: Dynamical Systems with Applications using Mathematica, Birkhäuser
 R. Abraham: C. Shaw: Dynamics: The Geometry of Behavior, Addison-Wesley
 S. Wiggins: Introduction to Applied Nonlinear Systems and Chaos, Springer
 S. Sastry: Nonlinear Systems: Analysis, Stability, and Control, Springer.