Geodesic
On connection between continuous and discontinuous neural field models with microstructure I. General theory
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 121, pp. 17-30

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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.
Keywords: mathematical neuroscience, neural field models with microstructure, solvability, continuous dependence on parameters. 
@article{VTAMU_2018_23_121_a2,
     author = {E. O. Burlakov and M. A. Nasonkina},
     title = {On connection between continuous and discontinuous neural field models with microstructure {I.} {General} theory},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {17--30},
     publisher = {mathdoc},
     volume = {23},
     number = {121},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_121_a2/}
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E. O. Burlakov; M. A. Nasonkina. On connection between continuous and discontinuous neural field models with microstructure I. General theory. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 121, pp. 17-30. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_121_a2/