ON CONNECTION BETWEEN CONTINUOUS AND DISCONTINUOUS NEURAL FIELD MODELS WITH MICROSTRUCTURE I. GENERAL THEORY


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Abstract

We suggest a method allowing to investigate existence and the measure of proximity between the stationary solutions to continuous and discontinuous neural fields with microstructure. The present part involves a theorem on solvability of such equations based on topological degree theory, and a theorem on continuous dependence of the solutions under the transition from continuous to discontinuous activation function using compactness in a special topology.

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Неокортекс человека - это верхний слой больших полушарий головного мозга, толщиной 2-4 мм, содержащий около 109 нейронов, имеющих 60 × 1012 связей [1].
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About the authors

Evgenii Olegovich Burlakov

Tambov State University named after G.R. Derzhavin

Email: eb_@bk.ru
PhD, Researcher at the Research and Educational Centre “Fundamental Mathematical Research” 33 Internatsionalnaya St., Tambov 392000, Russian Federation

Margarita Aleksandrovna Nasonkina

Tambov State University named after G.R. Derzhavin

Email: nasonkina.margo@gmail.com
Master’s Degree Student on Training Direction “Mathematics” 33 Internatsionalnaya St., Tambov 392000, Russian Federation

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