Physics – Biological Physics
Scientific paper
2006-07-27
Ann. Phys. (Leipzig) 16, 379 (2007)
Physics
Biological Physics
Dedicated to Hermann Haken on the occasion of his 80th birthday
Scientific paper
10.1002/andp.200610243
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.
Guessmann Martin
Pelster Axel
Wunner Guenter
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