Introduction to Complex Systems

Organizing institution
Utrecht University - Faculty of Science
Course code
Course fee (excl. housing)
€ 150.00
Advanced Bachelor

Our world has an abundance of complex systems. These are typically large collections of connected elements that influence each other. Examples are the brain; society; traffic; the financial system; interacting institutions; climate; ecosystems; interacting atoms or molecules; the World Wide Web. These diverse examples have surprisingly many features in common. As a rule, they show various properties that make a complex systems more than the sum of their parts. In this course, we combine examples across physics, the life sciences, socio-economic sciences and humanities with an introduction to basic mathematical tools to learn a complex systems way of thinking.

Diverse though these examples are, they have a surprisingly large number of features in common. As a rule, these systems have various properties that are more than the sum of their parts, i.e., emergent phenomena that cannot be explained by studying elements in isolation. For example, a traffic jam is an emerging property of interacting cars on a road that gets busier that cannot be explained even by the most detailed knowledge about how an individual car works or is operated. In addition, complex systems such as a network of interacting species in an ecosystem, or banks in a financial network, may be robust (stable) against disturbance, but in contrast may also be close to a tipping point (bifurcation) beyond which they fully collapse. Finally, the connectivity of components in complex systems, for example a network of interacting humans in social cyber-space may be such that an opinion, message or image goes "viral" in an apparently sudden, unpredictable and uncontrollable manner.

In recent decades, the science of studying complex systems has started to evolve and mature. It has become clear that a new, more integrated way of thinking is essential for understanding many of the complex challenges that humanity faces. The above mentioned set of shared features allow complex systems to be studied with a uniform collection of tools from mathematics and theoretical physics. Such a shared toolset paves the way for deriving general principles on the properties of complex systems across disciplines. Ultimately, the aim is to derive rules on how the dynamical behaviour of a complex system depends on the combined properties of individual elements, the nature of the interactions between elements, as well as the topology of interactions between elements, in order to understand and predict these systems and control them to have desirable properties. As an example, insight into which features of complex systems generate resilience against perturbations versus which properties enhance the sensitivity of the system and allow it to transition to a different equilibrium state is important for a broad range of questions on, for example, climate change, social-political change, disruptive innovations, infectious disease emergence and ecosystem collapse.

We focus on the four key aspects of complex systems examplified above: emergence, resilience, transitions and predictability and control. We demonstrate how they are recurring concepts in a broad range of areas ranging from the life sciences, social sciences, economics, as well as humanities; and thereby unify them at a deep level. We will stimulate the students to think in terms of these abstract unifying concepts across the diverse disciplines; illustrate the need for mathematical models to study and quantify these properties; and teach the students basic mathematical tools to study the behaviour of the constructed models.

The summer school is offered by researchers from the Complex Systems Studies.

Download the day-to-day programme (PDF)

Course director

Dr. Kirsten ten Tusscher

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.

Study load

Tutorial lectures in the morning; hands-on computer practice after lunch, guest lecture at the end of the afternoon from the broadest possible range of topics/fields/problems where complex systems play a role.


A limited number of partial fee-waiver scholarships is available for UU students. € 150.00
Housing € 200.00 , through Utrecht Summer School

A limited number of partial fee-waiver scholarships is available for UU students.


The budget for fee-waiving scholarships has been fully spent. Those of you who have already applied and have received this scholarship will have noted this from the reduced amount billed with regards to the Summerschool.

The scholarship for a travel grant has been rewarded. The rewarded applicants will be notified by email. If you receive no email this means you have not been rewarded a travel grant. We are aware that for some of you this means that they can not afford to come to the Summerschool, we are deeply sorry for this but unfortunately are limited in the budget we have available for travel grants. New applicants can no longer apply for a travel grant.

Required documents

For this course you are required to upload the following documents when applying:

More information

Prof. Kirsten ten Tusscher
E: K.H.W.J.tenTusscher@uu.nl
T: 030-2533637


Application deadline: 24 June 2018