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.