Research topics of the Schuster group

Deterministic Chaos:

Nonlinear dynamical systems show a sensitive behaviour (butterfly effect) both to changes in initial conditions and changes in system parameters. Research focuses on statistical properties, stability analysis, and stabilization of unstable periodic orbits.

Self-Organized Criticality and 1/f noise

In nature, nearly every system shows adaptive behaviour, but the phenomenon is far from being well understood. Especially we lack a comprehensive view on what these systems have in common and how completely different systems can show similar behaviour.
One interesting and challenging problem in evolution of species is the appearance of punctuated equilibrium and 1/f statistics. 1/f power spectra are quite often found, e.g. in earthquake and avalanche distributions, intermittency, resistor noise, aggregation processes, and quasar light.
Apart from studying models for these systems, a general paradigma is to be proven: that maximal complexity and most efficient adaptation is reached in a state of self-organized criticality at the border between order and chaos.
Some recent topics investigated in this field include:

Adaptive systems and Models of Evolution:
Neural Networks, Genetic Algorithms and Stochastic automata:

Motivated by the high computational abilities of the brain, many models of artificial neural networks have been investigated. Both the models themselves (in theoretical properties and biological modelling) and applications of various network architectures are under investigation: