Complex Systems Project

Course goals

at the end of the course the student will master or have acquired (working) knowledge in
- recognizing defining properties of complex systems, such as emergence, self-organization, transitions, resilience, and adaption
- applying basic terms of network theory
- manipulating computer models simulating complex systems and interpret the output data
- explaining how within a complex system the evolution is influenced by spatial patterns

Content

 ATTENTION !    CLASSES ON WEDNESDAYS IN MINNAERTGEBOUW ZAAL 4.16  FROM 13.15-17.00 u.
 LECTURE CLASS ON FRIDAYS  IN MINNAERTGEBOUW 4.16 FROM 9.00-10.45 u.

Complex Systems is a new and fast developing field of research. Its focus is on systems consisting of many interacting constituents and their collective behaviour. Common examples of such systems are the brain, cities, climate, ecosystems, economy, and traffic. While these systems seem vastly different on first sight they share many features. One of them is emergence, which describes the phenomenon that the sum of all parts does something which is very hard to predict from the the individual behaviour of the constituents. Connected to this one can often observe self-organization in complex systems. This means that structures emerge spontaneously from within without any influence from the outside world. These properties provide the backbone of this course and are recurring themes in a variety of contexts.
The course consists of three pillars chosen to familiarize the student with all properties of complex systems. After a short introductory part the first main part is network theory. Networks come in a variety of forms ranging from very ordered such as crystals to very disordered such as the internet. Networks provide the basis for modelling many complex systems. In a next part you will learn about the complexity of evolution in spatially extended ecosystems. This consists of an introduction to cellular automata and their relevance to simulating biological systems. Using a simple example you will learn how complicated spatial patterns can develop from simple interactions between individuals and how these cells backreact with the evolution of the organism. 
Finally, we discuss collaboration. In human (also true for some animals) communities. One can observe a large degree of collaboration, although for every individual, it would be in his or her interest to let the others do the work. We use computer models to study this conflict of interest.
This course uses computer programs coded in Python, although working knowledge in Python is no prerequisite. There will also be mathematical modelling for which VWO Wiskunde A or B is sufficient.
Every one of the three parts will be concluded with an exam and there will also be hand-in exercises. The course concludes with a report written over a small project carried out in a group.

The course is given on Wednesdays from 13.15-17.00 and Fridays 9.00-10.45 in Minaert 4.16. There is also an exercise session on Fridays from 11.00-12.45. See Osiris for the location.