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Steps toward numerical mode analysis of organizing systems
Junmei Zhu1, Christoph von der Malsburg
1Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438, Frankfurt am Main, Germany. jzhu@fias.uni-frankfurt.de
Abstract:
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.
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