Dynamical Systems and Non-Linear Dynamics
Full course description
The course Dynamical Systems and Nonlinear Dynamics will provide you an introduction into the analysis and visualization of the complex behavior of dynamical systems. We will look at a many features of nonlinear systems, starting from first-order differential equations, covering phase- plane analysis and eventually study the famous Lorenzequations.
Topics will include fixed points and stability, numerical methods, bifurcations, oscillators, attractors, chaos, fractals and recurrence analysis. The theory will be
supported by practical examples and applications, and assignments will be mostly done with the help of the computer, using MATLAB and/or Octave. Journal clubs/case studies
will provide further insight into various applications of dynamical systems theory in the field of Systems Biology.
Course objectives
Intended learning outcomes (ILO’s)
1. Describe the behavior of a low-dimensional nonlinear system by identifying its fixed points and classifying their stability
2. Explain how a change in a property of a system can lead to change in its behavior and categorize the type of change
3. Discover deterministic chaos in continuous- and discrete-time systems and compute the properties of a strange attractor
4. Create visualizations of the dynamical behavior of a system using various computational tools that illustrate fixed points, stability, periodicity and chaotic
behavior.
5. Summarize scientific publications that feature applications of nonlinear dynamical system analysis in systems biology and discuss the added value of the techniques
used.
Recommended reading
Mandatory Literature:
The course will be given following the material discussed in: Steven H. Strogatz, Nonlinear Dynamics and Chaos, 2nd edition. Students are strongly recommended to obtain a copy of this book, as it provides a gentle but thorough introduction into the analysis of nonlinear systems with many examples from physics, biology, chemistry and engineering.
Additional Literature:
Additional literature (journal clubs, background material) will be made available through the student portal.