Bifurcations describe qualitative changes in the long-term behavior of dynamical systems under
parameter variation. Such changes occur at so-called critical values and it is not only of imminent
importance to locate the critical values, but also to understand the precise nature of a bifurcation in
oder to fully comprehend time-variant phenomena. Among the zoo of all bifurcations, those of
Neimark-Sacker type are not only omnipresent in applications from e.g. the life sciences and
economics, but also require an interesting mathematical machinery for their analysis. Roughly
speaking, Neimark-Sacker bifurcations describe transitions from a point as object capturing the
long term behavior, to a disk containing more complex dynamics.
In the project at hand, we leave the classical framework of dynamical systems, where the law of
evolution is constant in time. We are rather interested in problems subject to an aperiodic temporal
forcing, which might be endogenous (seasonal effects) or exogenous (regulation, control). For
such problems many of the classical concepts (eigenvalues, equilibria) fail, but the recent theory of
nonautonomous dynamical systems provides an appropriate mathematical framework. More
detailed, our goals are to understand nonautonomous versions of the Neimark-Sacker bifurcation,
to develop tools required for their analysis, to identify possible new phenomena and to illustrate
them by means of applied problems.