Mathematical Modelling of Complex Systems

Lecture content:

Steps in the development of mathematical/computational techniques originated from the emerging interdisciplinary field of complex systems science to get insight into the function of the complex environmental systems.
The lecture consists of the following three blocks:

I Introduction:
-Complex systems in a nutshell
-Fundamentals of modelling

II Systems with a small number of variables
- Static models
- Continuous-time models/Box models
- Discrete-time models
- Bifurcations/Chaos

III Systems with a large number of variables
- Continuous-field models
- Turing instabilities
- Phase Transitions

Literature:
The course is self-contained, so there is no mandatory reading. The treatment of numerical methods of continuous-time and field models is based strongly on the book 'Numerical Recipes' by William H. Press, Saul Teukolsky, William T. Vetterling und Brian P. Flannery