Physics – Biological Physics
Scientific paper
2006-07-28
Ann. Phys. (Leipzig) 16, 395 (2007)
Physics
Biological Physics
Dedicated to Hermann Haken on the occasion of his 80th birthday
Scientific paper
10.1002/andp.200610244
We apply generic order parameter equations for the emergence of retinotopy between manifolds of different geometry to one- and two-dimensional Euclidean and spherical manifolds. 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 cell sheets. Our results for strings are analogous to those for discrete linear chains obtained previously by Haeussler and von der Malsburg. The case of planes turns out to be more involved as the two dimensions do not decouple in a trivial way. However, superimposing two modes under suitable conditions provides a state with a pronounced retinotopic character. In the case of spherical manifolds we show that the order parameter equations 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.
Guessmann Martin
Pelster Axel
Wunner Guenter
No associations
LandOfFree
Solutions of the Haeussler-von der Malsburg Equations in Manifolds with Constant Curvatures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Solutions of the Haeussler-von der Malsburg Equations in Manifolds with Constant Curvatures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solutions of the Haeussler-von der Malsburg Equations in Manifolds with Constant Curvatures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-250874