| Spiral waves have been observed in many chemical and biological systems as well as in reaction-diffusion equations that model such systems.Spiral waves can destabilize in various different ways: They can experience far-field instabilities or begin to meander and to drift. In this talk, I would like to give an overview of these phenomena and describe recent efforts to explain them. In particular, it is discussed how the different spectral properties of spiral waves on bounded disks versus the entire plane help to understand the above instabilities. This is joint work with Arnd Scheel. |