Preprint of the project:
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.
