Abstract
The purpose of this paper is twofold: First, we present a semi-quantitative nonlinear field theory of the brain under realistic anatomical connectivity conditions describing the interaction between functional units within the brain. This macroscopic field theory is derived from the quasi-microscopic conversion properties of neural populations occurring at synapses and somas. The quasi-microscopic models by Wilson-Cowan (1972,1973) and Nunez (1974) can be derived from these. Functional units are treated as inhomogeneities within a nonlinear one-dimensional neural tissue. Second, for the case of the Kelso experiment the field equation is treated analytically and numerically and can be reduced to a set of ordinary differential equations which corresponds to a model by Jirsa et al. (1994, 1995). This phenomenological model reproduces the spatio-temporal phenomena experimentally observed. Here the most prominent property of the neural tissue is the parametric excitation. The macroscopic field parameters can be expressed by quasi-microscopic neural parameters.
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