The development of the synaptic connections between two neural elds (e.g. retina and tectum) from an undi erentiated initial state toward a topological projection is described by an appropriate system of di erential equations. The equations are based simply on cooperative and competitive interactions between the individual synaptic contacts. In the case of one-dimensional elds it is shown that the system is able to select either of the two possible orientations and to produce a precise topological projection. This is done with the methods of synergetics: Linear analysis near the initial state, classi cation of the linear modes into principal and ancillary, adiabatic elimination of the latter from the original system and discussion of the resulting equations.
Generalized Ginzburg-Landau equations for phase transition-like phenomena in lasers, nonlinear optics, hydrodynamics and chemical reactions
Higher order corrections to generalized Ginzburg-Landau equations of non-equilibrium systems
C. Malsburg,et al.
How to label nerve cells so that they can interconnect in an ordered fashion.
Proceedings of the National Academy of Sciences of the United States of America.
R. M. Gaze.
The Problem of Specificity in the Formation of Nerve Connections
D J Willshaw,et al.
A marker induction mechanism for the establishment of ordered neural mappings: its application to the retinotectal problem.
Philosophical transactions of the Royal Society of London. Series B, Biological sciences.