In order to model processes in nature and engineering it is frequently required to know system states in the past. Mathematically this can be done by using delay differential equations (DDE). In contrast to ordinary differential equations (ODE) the associated phase-space is infinite-dimensional (the space of continuous functions defined on an interval [-r,0]). Due to the phase-space studying the dynamics of a DDE is a much harder task.
In our group we study the activity of a network consisting of a finite number of (biological) neurons. Taking into account the connection structure (inhibitory, excitatory) and signal propagation times (axonal, dendritic, synaptic) we obtain a system of delay differential equations.
Using analytical and numerical methods we determine the dynamics of such systems. We consider
This work is done in collobaration with Fotios Giannakopoulos
and Christian Hauptmann.
Dynamical systems
In addition to DDEs I am interested in general theory of
dynamical systems and bifurcation theory. Applying analytical
results and numerical algorithms it is possible to describe the
dynamical features of ordinary differential equations, discrete
maps, etc.
Home range analysis
Brand new project ! Using real data, statistical methods and simulations we try to estimate the home range of bats. More information will be given soon. In collaboration with Johannes Müller.
