Methods and Models in Complex Systems

Course goals

At the end of the course, the students are able to:

• recognize a Complex System when they encounter one
• understand key concepts in Complex Systems, such as Emergence, Evolution, Adaptation, Transition, and Resilience
• appreciate the role of model building for Complex Systems
• apply the knowledge of Complex System toolbox, such as Chaos Theory, Agent Based Modeling, Pattern Formation and Network Theory to problems, and
• program in Python and interpret results

Assessment
Exam.

Prerequisites
VWO mathematics level B. Programming ability is not necessary, but will be useful.
Student should be able to compute derivatives, integrals, multiply two small matrices, solve a system of linear equations, be familiar with a notion of the determinant of a matrix, and know basic trigonometry.
Programming in Python is an advantage but is not compulsory. Getting to grips with Python, if needed, will be facilitated in the course.

Students who are registered followers of the Minor Complex systems (MINOR-CS-WIS) will be admitted directly to this course. All other students will be placed on the waiting list, to be admitted after the registration period if there are enough places available.

Content

Complex Systems is a relatively young, interdisciplinary, and rapidly developing field. The hallmark of Complex Systems is that they consist of many interacting components. Examples of Complex Systems are the brain, an ant colony, an urban area, the climate, an ecosystem, the economy and traffic.

Although these topics as first sight have little in common, deep down they share a lot of common features. One of them being emergence of collective behaviour, the phenomenon that the system, as a whole, exhibits characteristics that are not simple copies of the characteristics of the components. One also often sees self-organization in Complex Systems: (spatial) structures that spontaneously arise without external influence. These, and related properties form the common thread of this course.

The course will be taught in English.

The course comes in three modules. Sequentially these are:

• Introduction to Complex Systems, Chaos Theory, Agent Based Modeling, and Python
• Cellular Automata, Emergence of Patterns, Genetic Algorithms and
• Network Science.

In general terms, the students will:

• program in Python
• build mathematical models
• solve exercises, and
• write scientifically.

Course form
Lectures, tutorials.

Literature

• H.Sayama,"Introduction to the modelling and analysis of Complex Systems", https://textbooks.opensuny.org/introduction-to-the-modeling-and-analysis-of-complex-systems/ 
• Steven H. Strogatz, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering", second edition(!) CRC Press 2015.