On the conjecture of Miklós Farkas: Bifurcation of time-periodic pattern in reaction diffusion systems

One of the fascinating properties of reaction-diffusion systems is the variety of special types of solutions they exhibit. Certain systems of this type can have for example travelling waves or rotating wave solutions, furthermore via bifurcation analysis one can show new class of solutions. This talk is about the possibility the occurrence of time periodic solution (time periodic pattern) of reaction-diffusion systems when the kinetic system, i.e. the system without the diffusion term exhibits periodic solution, as well. We look into the question whether the usual result regarding Turing bifurcation can be replaced by some other one.