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Introduction to Complex Systems (2026/2027: Semester 2)
Cursusdoel
Er is geen informatie over het cursusdoel bekend.
Vakinhoudelijk
Schedule. Wednesday 17:15-19:00.
In recent years there has been 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. Emergence, synchronization, entropy, large deviations, resilience of complex systems, critical transitions. Applications in biology, climate science, economics, sociology, innovation science.
Prerequisites. Familiarity with elementary concepts from linear algebra (eigenvalues), dynamical systems and probability. Programming in mathematical software (Matlab, Mathematica).
In recent years there has been 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. Emergence, synchronization, entropy, large deviations, resilience of complex systems, critical transitions. Applications in biology, climate science, economics, sociology, innovation science.
Prerequisites. Familiarity with elementary concepts from linear algebra (eigenvalues), dynamical systems and probability. Programming in mathematical software (Matlab, Mathematica).
Werkvormen
Hoorcollege
Toetsing
Eindresultaat
Verplicht | Weging 100% | ECTS 7,5
Ingangseisen en voorkennis
Ingangseisen
Je moet een geldige toelatingsbeschikking hebben
Voorkennis
Er is geen informatie over benodigde voorkennis bekend.
Voertalen
- Engels
Cursusmomenten
Tentamens
Er is geen tentamenrooster beschikbaar voor deze cursus
Verplicht materiaal
Er is geen informatie over de verplichte literatuur bekend
Aanbevolen materiaal
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BOEKMay, R.M., Stability and Complexity in Model Ecosystems, Princeton University Press, 1973.
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BOEKScheffer, M., Critical Transition in Nature and Society, Princeton University Press, 2009.
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BOEKNowak, M., Supercooperators, Free Press, 2012.
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SOFTWAREUA10190 Matlab 2013a
Coördinator
| dr. C. Spitoni | C.Spitoni@uu.nl |
Docenten
Inschrijving
Deze cursus is open voor bijvakkers. Controleer wel of er aanvullende ingangseisen gelden.
Inschrijving
Van maandag 2 november 2026 tot en met vrijdag 20 november 2026
Na-inschrijving
Van maandag 18 januari 2027 tot en met maandag 22 februari 2027
Inschrijving niet geopend
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