Regensburg 2004 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 34: Nonlinear Dynamics and Chaos I
DY 34.5: Vortrag
Mittwoch, 10. März 2004, 15:30–15:45, H2
Retinotopic Projections between Discrete Euclidean Manifolds — •Martin Güßmann1, Axel Pelster2, and Günter Wunner1 — 1Institut für Theoretische Physik 1, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart — 2Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin
In the course of ontogenesis of vertebrate animals well-ordered neural connections are established between retina and tectum, a part of the brain which plays an important role in processing optical information. As a result of this self-organization process a retinotopic projection is formed, i.e. neighbouring retinal cells project onto neighbouring cells of the tectum. We generalize the model of Ref. [1] to obtain order parameter equations for the connection strengths between two manifolds of arbitrary geometry. Here we consider the case of discrete n-dimensional Euclidean manifolds. For the linear chain we are interested in the question under which circumstances retinotopic or non-retinotopic modes become unstable. Furthermore, we investigate the generation of retinotopic projections between two planes. An important result consists in the fact that this case cannot be reduced to two linear problems, i.e. there is no trivial decoupling of the two dimensions. The existence of a potential dynamics of the order parameters is discussed in detail.
[1] A.F. Häussler and C. von der Malsburg, J. Theoret. Neurobiol. 2, 47 (1983)