Current Research

Coupled dynamics and quiescent phases
Consider an ecological model with two species where the global dynamics is completely understood. Suppose each species goes quiescent at random times, i.e. each compartment is diffusely coupled to a quiescent phase, equivalently, the vector field is diffusely coupled to the zero field. Can one predict how the dynamics changes? Does a stable stationary point or limit cycle stay stable? (Work with Thomas Hillen).

Distributed exit times
In most biological models it has been assumed that the transition from one compartment to another is gouverned by poisson processes. How does the dynamic change if the exit times are not exponetially distributed? (Work with Frithjof Lutscher).

Neutral delay equations and state dependent delays
It is known that certain structured population models of Gurtin-MacCamy type can be reducted to neutral delay equations. The delay corresponds to the duration of the juvenile phase. If the latter depends on the total adult population then one arrives at state dependent delay equations. (Work with Christina Kuttler and Maria Barbarossa).

Granular matter
In 1999 Christina Kuttler and KPH have designed their two layer model for the deposition of granular matter. At present we (with Dirk Schieborn) try to connect this model to viscous eikonal equations.

Qualitative behaviour of Cellular Automata
(Work with Joannes Müller).