Abstract. We here are pointing out a basically well-known pathway to the analysis of self-organizing systems that is now well in reach of numerical methods. Systems of coupled nonlinear differential equations are decomposed into normal modes, are reduced by adiabatic elimination of stable modes to a much smaller system of unstable modes and their nonlinear interaction. In the past, this treatment was accessible only for highly idealized model systems. Guided by an application to retinotopic map formation we discuss the extension to more realistic cases. 1

A linear neural network is proposed for mamalian vision system in which backward connections from the primary visual cortex (V1) to the lateral geniculate nucleus play a key role. The backward connections control the flow of information from the LGN to V1 in such a way as to maximize the rate of transfer of information from the LGN to V1. The application of hebbian learning to the forward and backward connections causes the formation of receptive fields which are sensitive to edges, bars, and spatial frequencies of preferred orientations. Receptive field types in V1 are shown to depend on the density of the afferent connections in the LGN. Orientational preferences are organized in the primary visual cortex by the application of lateral interactions during the learning phase. Change in the size of the eye between the immature and mature animal is shown be an important factor in the development of V1 organization. The orgainization of the mature network is compared to that found in the macaque monkey by several analytical tests. 1