**Disciplines/fields: **All fields where you want/need to model temporal processes.

**Duration:** 4 sessions

### Course Content

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.

### Objectives

Get an overview and an intuition of the many (maaaaany!!) ways of how one can formalize temporal development.

### Literature

There exists no standard textbook or tutorial with a similar scope as this tutorial (more precisely, I don't know any). The course materials contain extensive references for the various parts of the tutorial, with an emphasis on tutorial texts.

### Vita

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). Since 2003 he is Associate Professor for Computational Science at Jacobs University Bremen. His research interests is the computational modelling of hierarchical, nonlinear, neural (or just plain computational) learning systems with applications in pattern recognition, engineering and cognitive/robot modelling.