Self-Organized Formation of Retinotopic Projections Between Manifolds of Different Geometries -- Part 3: Spherical Geometries

We follow our general model in Ref. [3] and analyze the formation of retinotopic projections for the biologically relevant situation of spherical geometries. To this end we elaborate both a linear and a nonlinear synergetic analysis which results in order parameter equations for the dynamics of connection weights between two spherical cell sheets. We show that these equations of evolution provide stable stationary solutions which correspond to retinotopic modes. A further analysis of higher modes furnishes proof that our model describes the emergence of a perfect one-to-one retinotopy between two spheres.