Email this article ON CONNECTION BETWEEN CONTINUOUS AND DISCONTINUOUS NEURAL FIELD MODELS WITH MICROSTRUCTURE I. GENERAL THEORY
- Authors: Burlakov E.O.1, Nasonkina M.A.1
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Affiliations:
- Tambov State University named after G.R. Derzhavin
- Issue: Vol 23, No 121 (2018)
- Pages: 17-30
- Section: Articles
- URL: https://ogarev-online.ru/2686-9667/article/view/297207
- DOI: https://doi.org/10.20310/1810-0198-2018-23-121-17-30
- ID: 297207
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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].×
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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