Dynamical Systems: a Navigation Guide

Teacher: Herbert Jaeger (University of Groningen)

This lecture-series gives a broad overview over the zillions of formal models and methods invented by mathematicians and physicists for describing “dynamical systems”.

Here is a list of covered items:

Finite-state automata with and without input, deterministic and non-deterministic, probabilistic), hidden Markov models and partially observable Markov decision processes, cellular automata, dynamical Bayesian networks, iterated function systems, ordinary differential equations, stochastic differential equations, delay differential equations, partial differential equations, (neural) field equations, Takens’ theorem, the engineering view on “signals”, describing sequential data by grammars, Chomsky hierarchy, exponential and power-law long-range interactions, attractors, structural stability, bifurcations, phase transitions, topological dynamics, nonautonomous attractor concepts.

All of this is useful for modeling cognitive dynamics at some level of abstraction. In the lectures, I try to work out the underlying connecting lines between the “dots” listed above.

Contrary to the other topics, there will be no hands-on assignments for this lecture series.

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