Action potentials in action: pulse waves in partial differential equations

(Prof. Dr. Jens Rademacher)

Action potentials act as information bits in neurons and appear more generally in so-called excitable media, such as heart tissue, reactive gels and surface catalysis. In spatially one-dimensional mathematical models single action potentials are pulse waves, that are constant in a moving coordinate. The information transfer can be disturbed by interaction between pulses and splitting pulses. This has been observed numerically in various models, in particular the famous FitzHugh-Nagumo equation.

In the project these numerical studies will be explored further and connected to mathematical questions. You will obtain insight into a hot research topic and learn methods for the mathematical study of pulse waves.