Netherlands, Utrecht

Introduction to Complex Systems

when 24 August 2015 - 28 August 2015
duration 1 week
credits 1.5 EC
fee EUR 350

Our world has an abundance of so-called complex systems. They are typically very large collections of interacting individual elements. Examples range across all levels of organisation and across the biological, physical, social and "silico" world. We can think of interacting genes or cells in the human body or the neurons that make up the brain; interacting humans transmitting an infectious disease, or sharing rumours, ideas, opinions, innovations; interacting cars in traffic; interacting financial institutions, companies, governmental organisations or governments; the climate; interacting species in an ecosystem; interacting atoms or molecules; the World Wide Web.

Diverse though these examples are, they have a surprising number of features in common. As a rule, these systems have dynamic properties that are more than the sum of their parts, i.e., phenomena can occur or emerge that cannot be explained by studying elements in isolation. For example, a traffic jam is an emerging property of a road that gets busier that cannot be explained even by the most detailed knowledge about how an individual car works or is operated. A network of interacting species in an ecosystem, or banks in a financial network, can have the property that it is robust or stable against disturbance. A network of interacting humans in social cyber-space may be connected in such a way that an opinion, message or image goes "viral", apparently suddenly.

Such features allow these systems to be studied with a uniform collection of tools from mathematics and theoretical physics. This paves the way for the formulating general principles and a robust insight into how diverse phenomena and properties can be derived, understood, and ultimately predicted and mitigated from knowledge on not only the elements, but importantly also on how they are connected and interact. Only by studying the whole can we be able to make sense of what is observed in such systems, and can we gain understanding of how systems can be better designed to have the desired properties. Additionally, insight into which features of complex systems allow for disruption and changes to a different equilibrium state is important for a broad range of questions on, for example, climate change, social-political change, disruptive innovations, and infectious disease emergence. In recent decades, a science of studying complex systems has started to evolve and mature. It has become clear that a new and more integrated way of thinking is essential for understanding many of the complex challenges that humanity faces, from a societal, environmental and scientific point of view.

We focus on four key aspects of complex systems: emergence, resilience, transitions and control. We demonstrate how they are, in fact, recurring concepts in a broad range of areas, drawn from research problems in life sciences, social sciences, economics, as well as humanities; and thereby unify them at a deep level. Across diverse disciplines we stimulate the students to think in terms of these abstract unifying concepts; building up to the need to construct mathematical models in order to quantify them; and to further use basic mathematical tools to study the models.

Course leader

Dr. Debabrata Panja

Target group

Reference level starts at end of bachelor for academic maturity, but for the rest is open to students from all backgrounds and subjects. The audience is expected to have an interest in and the capacity for understanding abstract notions and reasoning. A mathematical background is not required, but the lectures and practical work do lean heavily on working knowledge of mathematics at end of secondary school level (linear algebra, functions, differential equations).

Course aim

The aim of the course is: i) to recognise complex systems related to societal, environmental, engineering and scientific problems and to learn their basic features, ii) to introduce a complex systems way of thinking and analysis, iii) to learn basic mathematical concepts and methods needed for complex system analysis, for example from dynamical systems theory and the theory of networks, iv) to get hands-on experience in studying complex systems.

Credits info

1.5 EC
+ certificate of attendance

Fee info

EUR 350: Including housing
EUR 150: Excluding housing


Utrecht Summer School doesn't offer scholarships for this course.

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