Preprint des Projektes: Forschungsschwerpunkt Mathematisierung

Numerische Analyse Strukturbildender Prozesse

165 Thorsten Hüls.
Instability helps virtual flies to mate

In this paper we perform a bifurcation analysis for a discrete time dynamical system, describing the behavior of a virtual fly, developed by Böddeker and Egelhaaf. Like real blowflies, the virtual counterparts exhibit a dichotomous behavior: they catch small targets but follow big objects in a constant distance. We consider this model for targets on linear and on circular trajectories. Then we transform the system into a "frozen" form, such that the position of the target is fixed. It turns out that the loss of stability of a fixed point in the frozen system due to a Neimark-Sacker bifurcation, explains the dichotomous behavior of the virtual fly.