Modelling Critical Transitions

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Modelling critical transitions in nature and society

To be announced


Recently it has become clear that many systems may go through critical transitions or tipping points. Not only ecosystems, but also the climate, depressed patients and financial markets may suddenly undergo dramatic change. After a tipping point it may be difficult or impossible to restore the original situation. Therefore, there is a strong need to predict the occurrence of such transitions beforehand. Recently we have made much progress by the identification of generic indicators of the proximity to a tipping point, so-called early warning signals. This theory has been developed using mathematical models of various complexity. In this course you will learn the theory of critical transitions and how to apply this in your own study. It will involve an intensive course on the analysis of mathematical models, and an introduction in early warning signals. The second part of the course consists of (making a plan) how to apply modelling or tipping points in your own work.

After the course the student:

  • Can analyse simple and more complex differential equation models by simulation and use the results in publications
  • Knows how to link dynamical systems theory to practice
  • Can adapt multi-species models and create spatial explicit models (cellular automata and lattice differential equations)
  • Can apply the theory of critical transitions and early warning signals
  • Understands when deterministic chaos can be expected
  • Can create a simple differential equation model based on a problem
  • During the course week: Training in modelling of critical transitions and chaos by lectures, computer practicals, walks, and discussions on own modelling challenges.
  • During the week after the course: Return day (or contact by email) for individual supervision on modelling challenges of your own research.
General information
Target Group The course is aimed at PhD candidates and other academics
Group Size Max. 30 participants
Course duration 1 week (+ a return day or contact by email in the week after the course)
Language of instruction English
Frequency of recurrence Every two years
Number of credits 2 ECTS
Lecturers Prof. Marten Scheffer and Dr. Egbert van Nes (Aquatic Ecology and Water Quality Management Group, Wageningen University)
Prior knowledge Basic knowledge of differential equation models and numerical integration. Some knowledge of MATLAB may be helpful. No emphasis on mathematics, but more simulation and use of models in practice.
Location To be determined


Fees 1

Generally, the following fees apply for this course, but note that the actual fees may be somewhat different for the next edition of this course.

PE&RC / WIMEK / WASS/ EPS / VLAG / WIAS PhD candidates with an approved TSP € 200,-
All others PhD candidates € 400,-
Post-docs and staff of PE&RC and WIMEK

1 The course fee includes a reader, full board, and accommodation.
2 Those defending their thesis at Wageningen University 
and those that are a member of IBED Amsterdam or VU Amsterdam

More information


Dr. Lennart Suselbeek (PE&RC)
Phone: +31 (0) 317 485426


This course is currently closed for registration, and will re-open once a new edition of this course is scheduled.