Since the task is to stop the fovea as soon as a certain detail
of the environment is focussed, one can draw
an interesting
analogy to static equilibrium networks (like e.g. the
Hopfield network, or the
Boltzmann machine). To see this, consider the whole
combined system consisting of
retina, controller, and pixel plane: A given weight vector
for 
together with a given visual scene defines an
`energy landscape' where the attractors should correspond to
solutions for the target detection task.
The main difference to conventional equilibrium networks is the fact that the dynamic equilibrium corresponding to a certain attractor involves external feedback. A mathematical analysis of such energy landscapes seems to be difficult, since it has to take domain-dependent details of the environment into account.