Instabilities in a continuous medium model for the retina

The shape of the spatial response of the retina on a small light stimulus as found by Rodieck (1965) for the cat, and proposed for the human retina among others by Korn and von Seelen (1972), resembles a Mexican hat known as a sombrero. A model presented by Röhler (1976), using a continuous medium as a description of the retina, can lead to such a "Mexican hat" response function for a specific choice of parameters. The spatial Fourier transform of this response function has a general appearance that corresponds to that calculated for stationary signals. However, such an analysis of the model for stationary signals is incomplete. Inspection of the time-dependent equations shows that it is unstable precisely for those parameter values that give the stationary response function its desired shape. Such stationary situations cannot be physically realized since the model is unstable.