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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2019 Volume 165, Pages 10–20 (Mi into463)

On continuous and discontinuous models of neural fields

E. O. Burlakova, T. V. Zhukovskayab, E. S. Zhukovskiyc, N. P. Puchkovb

a Tyumen State University
b Tambov State Technical University
c Tambov State University named after G.R. Derzhavin

Abstract: This paper is devoted to research in mathematical neurobiology whose purpose is the establishment of a connection between approaches to the modeling of neural fields based on continuous and discontinuous equations. We review works on this topic and propose a new method for solving such problems based on Volterra's abstract inclusions, which allows one to generalize some previously obtained results.

Keywords: mathematical model, neural field, integral equation, Hammerstein equation, solvability, continuous dependence on parameters.

UDC: 517.988, 517.968

MSC: 47J05, 47H04, 35R09, 45K05, 47H30, 92F99

DOI: 10.36535/0233-6723-2019-165-10-20



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