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wism484 - introduction to complex systems

time and place

Semester 1: 22 Sep 2015 – 19 Jan 2016
Time: Tuesdays, 13.15–15.00
See weekly schedule at the bottom of this page for exceptions to these dates.

Location: Changes rather a lot, see Osiris


Insructor: Jason Frank
Office: HFG 612
Tel: 030 253 2459

study load

ECTS : 7.5 studiepunten


There is a growing interest in the science of complex systems. A complex systems is loosely defined as one whose collective dynamical behavior cannot be readily deduced by a reductive study of its individual components. For example, it is difficult to predict where traffic jams will occur by studying the behavior of individual drivers, or to understand turbulence in water by studying the behavior of water molecules.

Important questions are how coherent collective behavior emerges in seemingly random systems, how complex systems undergo change, what makes certain behavior more or less stable. In this course we will study mechanisms for emergence, including synchronization and pattern formation, and mechanisms for transitions between system regimes, with an emphasis on analytical and computational methods. We will ask, what are the mathematical foundations of complexity science? What aspects of complex systems can we model successfully with mathematics, and where do we fall short?

Topics. Modeling techniques for complex systems: dynamical systems, games, networks, cellular automata, agent-based models, genetic algorithms; Emergent phenomena, synchronization, entropy and pattern formation. Applications in biology, climate science, economics, sociology, innovation science, physics.

Prerequisites. Familiarity with basic concepts of linear algebra (matrices, vectors, eigenvalue problems), dynamical systems (maps, differential equations), and elements of probability. Programming in mathematical software (Matlab, Mathematica).


Lectures will alternate between introductory treatments of modeling aspects of complex systems and guest lectures by researchers from different disciplines.
Guest lectures: (see schedule below)

Learning goals with assessment weighting

  • read and demonstrate (in class discussions) understanding of multidisciplinary literature (20%)
  • understand and apply mathematical methods and analysis to carry out and write two project reports involving computer simulation (50%)
  • demonstrate understanding of theoretical concepts on final exam (30%)

course material

We will draw on material from the following texts:

  • John H. Miller and Scott E. Page, Complex Adaptive Systems: An introduction to computational models of social life, Princeton University Press, 2007.
  • Nino Boccara, Modeling Complex Systems, 2nd edition, Springer, 2010. (This book can be freely read online by logging in to the UU Library and going to Springerlink.)
  • Claudius Gros, Complex Adaptive Systems: A primer, 4th edition, Springer, 2015. (This book can be freely read online by logging in to the UU Library and going to Springerlink.)
  • Kim Christensen and Nicholas Moloney, Complexity and Criticality, World Scientific Press, 2005.
  • Dirk Helbing, Social Self-Organization: Agent-based Simulations and Experiments to Study Emergent Social Behavior, Springer, 2012.

Matlab codes. Selected codes can be consulted in the repository.


  • Due to travel commitments of the instructor, there will be no classes during the first two weeks of the semester

  • 22 September (BBG 401).
    Introduction, course description, Lyapunov exponents.

  • 29 September (MIN 018).
    Emergence I: Synchronization of oscillators (Ch. 9 of Gros).

  • 6 October (BBG 401).
    Emergence II: Statistical Mechanics and Phase Transitions.
    Chapter 3 of A brief introduction to classical, statistical and quantum mechanics by O. Bühler.

  • 13 October (BBG 401).
    Emergence II: Statistical Mechanics and Phase Transitions (continued)
    See also: Information Theory Primer by Thomas Schneider.

  • 20 October (BBG 401).
    Emergence III: Pattern formation in reaction diffusion systems

  • 27 October (BBG 401). Guest lecture: Henk Stoof (Physics)

  • 3 November (OL 260).
    Cellular automata and self-organized criticality (tentative).
    See also: Principles of the self-organizing system by W. Ross Ashby.

  • 10 November (OL 260). Guest lecture: Vincent Buskens (Sociology)

  • 17 November (OL 260). Guest lecture: Rob de Boer (Theoretical Biology)

  • 24 November (OL 260). Guest lecture: Gábor Péli (Economics)
    Slides. Related article.

  • 1 December (OL 260).
    Information theory and coherent structures in fluids.

  • 8 December (OL 260).
    Agent-based models and evolution (tentative).
    Project 3 description, Due: 19 January, 13.15

  • 15 December (OL 260). Guest lecture: Henk Dijkstra (Oceanography and climate)

  • 5 January (OL 260). Guest lecture: Koen Frenken (Innovation studies)

  • 12 January (OL 260).
    Multiscale modelling (tentative).

  • 19 January (OL 260).
    Project 3 presentations.