Geodesic
On continuous and discontinuous models of neural fields
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 10-20

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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. 
@article{INTO_2019_165_a1,
     author = {E. O. Burlakov and T. V. Zhukovskaya and E. S. Zhukovskiy and N. P. Puchkov},
     title = {On continuous and discontinuous models of neural fields},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {10--20},
     publisher = {mathdoc},
     volume = {165},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_165_a1/}
}
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E. O. Burlakov; T. V. Zhukovskaya; E. S. Zhukovskiy; N. P. Puchkov. On continuous and discontinuous models of neural fields. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 10-20. http://geodesic.mathdoc.fr/item/INTO_2019_165_a1/