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Russian Universities Reports. Mathematics, 2024, Volume 29, Issue 145, Pages 43–50
DOI: https://doi.org/10.20310/2686-9667-2024-29-145-43-50
(Mi vtamu312)
 

This article is cited in 2 scientific papers (total in 2 papers)

Scientific articles

On well-posedness of a mathematical model of evoked activity in the primary visual cortex

E. O. Burlakovab, V. M. Verkhlyutovc, I. N. Malkov

a Tyumen State University
b Derzhavin Tambov State University
c Institute of Higher Nervous Activity and Neurophysiology of RAS
Full-text PDF (571 kB) Citations (2)
References:
Abstract: We propose a mathematical model that formalizes the macro- and meso-level dynamics of electrical potentials in the primary visual cortex of subjects, which corresponds to the presentation of visual stimuli to them. The mathematical framework is based on a two-layer neural field model, represented by a system of integro-differential equations, where the deep layer of the neural field models electrical activity that does not depend directly on the spatial orientation of the visual stimuli, whereas the activity of the superficial layer is sensitive to spatially oriented stimuli. The experimental design of presenting a series of visual stimuli is formalised in the present study in terms of an impulse control problem for the aforementioned two-layer neural field model. We propose a special metric space for construction of a unique solution to the control problem under standard assumptions for mathematical neurobiology regarding the functions involved in the modeling equations. We formulate sufficient conditions for continuous dependence of the solutions on the impulse control.
Keywords: integro-differential equations, nonlinear integral equations, bi-laminar neural field model, impulsive control, well-posedness
Funding agency Grant number
Russian Science Foundation 22-21-00756
The research was supported by the Russian Science Foundation (project no. 22-21-00756, https://rscf.ru/en/project/22-21-00756/).
Received: 20.09.2023
Accepted: 11.03.2024
Document Type: Article
UDC: 517.988, 517.968, 51-76
MSC: 37N25, 34K35
Language: Russian
Citation: E. O. Burlakov, V. M. Verkhlyutov, I. N. Malkov, “On well-posedness of a mathematical model of evoked activity in the primary visual cortex”, Russian Universities Reports. Mathematics, 29:145 (2024), 43–50
Citation in format AMSBIB
\Bibitem{BurVerMal24}
\by E.~O.~Burlakov, V.~M.~Verkhlyutov, I.~N.~Malkov
\paper On well-posedness of a mathematical model of evoked activity in the primary visual cortex
\jour Russian Universities Reports. Mathematics
\yr 2024
\vol 29
\issue 145
\pages 43--50
\mathnet{http://mi.mathnet.ru/vtamu312}
\crossref{https://doi.org/10.20310/2686-9667-2024-29-145-43-50}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian Universities Reports. Mathematics
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    References:23
     
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