Steps toward numerical mode analysis of organizing systems.
A well established method to analyze dynamical systems described by coupled nonlinear differential equations is to determine their normal modes and reduce the dynamics, by adiabatic elimination of stable modes, to a much smaller system for the amplitudes of unstable modes and their nonlinear interactions. So far, this analysis is possible only for idealized symmetric model systems. We aim to build a framework in which realistic systems with less symmetry can be analyzed automatically. In this paper we present a first example of mode analysis with the assistance of numerical computation. Our method is illustrated using a model system for the ontogenesis of retinotopy, and the results reproduce those from theoretical analysis precisely. Aspects of organization generalized from this model system are discussed.
Zhu
Junmei
J
Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438, Frankfurt am Main, Germany. jzhu@fias.uni-frankfurt.de
von der Malsburg
Christoph
C
D000818:Animals; D001921:Brain / Q000502:physiology; D005583:Fourier Analysis; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D008959:Models, Neurological; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D049490:Systems Biology