Lecturer: Herbert Jaeger
Fields: Interdisciplinary methods basics
Content
This is a crash course on dynamical systems, held at the Interdisciplinary College already several times – there is a demand! The presentation is meant to be introductory, understandable for a general natural / neural / cognitive science audience. Here is the planned schedule:
Session 1: Part I: Introduction: so many ways to classify models of dynamical systems! – Part II: A zoo of finite-state models: finite-state automata with and without input, deterministic and non-deterministic, probabilistic), hidden Markov models and partially observable Markov decision processes.
Session 2: Finite-state models continued: Cellular automata, dynamical Bayesian networks. Part III: A zoo of continuous state models: iterated function systems, ordinary differential equations, stochastic differential equations, delay differential equations, partial differential equations, (neural) field equations. Part IV: What is a state? Takens’ theorem.
Session 3: Part V: State-free models of temporal systems. The engineering view on “signals”. Describing sequential data by grammars. Chomsky hierarchy. Exponential and power-law long-range interactions. Part VI: qualitative theory of dynamical systems. Attractors, structural stability.
Session 4: Part VI continued: bifurcations. Phase transitions. Topological dynamics. Discussion: attractors and symbols. Part VII: non-autonomous dynamical systems. Basic definitions. Nonautonomous attractor concepts.
Literature
- Literature: The slides from the 2021 presentation https://www.ai.rug.nl/minds/uploads/IntroDynSys_IK_2021.pdf contain numerous references to (mostly introductory) materials, sorted by topic.
Lecturer
Herbert Jaeger studied mathematics and psychology at the University of Freiburg and obtained his PhD in Computer Science (Artificial Intelligence) at the University of Bielefeld. After a 5-year postdoctoral fellowship at the German National Research Center for Computer Science (Sankt Augustin, Germany) he headed the “Intelligent Dynamical Systems” group at the Fraunhofer Institute for Autonomous Intelligent Systems AIS (Sankt Augustin, Germany). From 2003 to 2019 he was Associate Professor for Computational Science at Jacobs University Bremen, and since 2019 he is Full Processor for Computing in Cognitive Materials at the University of Groningen. His current research revolves around formal theory-building for non-digital computing.
Affiliation: University of Groningen (NL)
Homepage: https://www.ai.rug.nl/minds/