  We generalize a model of Haeussler and von der Malsburg which describes the
self-organized generation of retinotopic projections between two
one-dimensional discrete cell arrays on the basis of cooperative and
competitive interactions of the individual synaptic contacts. Our generalized
model is independent of the special geometry of the cell arrays and describes
the temporal evolution of the connection weights between cells on different
manifolds. By linearizing the equations of evolution around the stationary
uniform state we determine the critical global growth rate for synapses onto
the tectum where an instability arises. Within a nonlinear analysis we use then
the methods of synergetics to adiabatically eliminate the stable modes near the
instability. The resulting order parameter equations describe the emergence of
retinotopic projections from initially undifferentiated mappings independent of
dimension and geometry.
