Project C3: Nonlinear excitation waves in neural systems.

Individual neuronal subunits can show bi- or multi-stability, excitable, or oscillatory
nonlinear dynamics. Spreading depolarization is essentially a reaction-diffusion pro-
cess, but as neurons are in addition interconnected nonlocally, wave propagation in
media with long-ranged spatial coupling will be investigated. Furthermore, subunits
or their communication path can be subject to noise or other effects, such as propa-
gation delays, which can introduce further complex bifurcation scenarios. We intend
to investigate the emergence, the dynamics and the stability of travelling waves
(excitable kinetics) and transient wave segments (subexcitable regime). Research
includes the analysis of the bifurcation scenarios between non-excitable,  subexci-
table and excitable local kinetics in the deterministic case and in the presence of
external noise, as well as the impact of the cortex geometry.
The phenomena will be analysed using generic models for excitable media and neu-
ral dynamics as the FitzHugh-Nagumo or the Hindmarsh-Rose model, but also nor-
mal forms close to bifurcations under consideration. Simultaneously, recent achieve-
ments in the theoretical understanding of transient wave segments in the framework
of the kinematical description of weakly excitable media will be applied to neural
dynamics. The investigations will also include the application of continuation tech-
niques for the determination of the stability of the nonlinear waves and numerical
bifurcation analysis.

Project leaders: Prof.Dr.  H. Engel [1],  Prof.Dr.  E. Schöll