Derivation of nonlinear amplitude equations for the normal modes of a self-organizing system

We here are pointing out a basically well-known pathway to the analysis of self-organizing systems that is now well in reach of nu- merical methods. Systems of coupled nonlinear differential equations are decomposed into normal modes, are reduced by adiabatic elimination of stable modes to a much smaller system of unstable modes and their nonlin- ear interaction. In the past, this treatment was accessible only for highly idealized model systems. Guided by an application to retinotopic map formation we discuss the extension to more realistic cases.

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