Geodesic
On existence and stability of ring solutions to Amari neural field equation with periodic microstructure and Heaviside activation function
Vestnik rossijskih universitetov. Matematika, Tome 27 (2022) no. 140, pp. 318-327

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In the present research, existence and stability of ring solutions to two-dimensional Amari neural field equation with periodic microstructure and Heaviside activation function are studied. Results on dependence of the inner and the outer radii of the ring solutions are obtained. Necessary conditions for existence and sufficient conditions for non-existence of radial travelling waves are formulated for homogeneous neural medium and neural media with mild periodic microstructure. Theoretical results obtained are illustrated with a concrete example based on a connectivity function commonly used in the neuroscience community.
Keywords: mathematical neuroscience, neural field models with microstructure, two-dimensional neural field equation, ring solution, stability of solutions, radial travelling waves.
Mots-clés : existence of solutions 
@article{VTAMU_2022_27_140_a1,
     author = {R. Atmania and E. O. Burlakov and I. N. Malkov},
     title = {On existence and stability of ring solutions to {Amari} neural field equation with periodic microstructure and {Heaviside} activation function},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {318--327},
     publisher = {mathdoc},
     volume = {27},
     number = {140},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2022_27_140_a1/}
}
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R. Atmania; E. O. Burlakov; I. N. Malkov. On existence and stability of ring solutions to Amari neural field equation with periodic microstructure and Heaviside activation function. Vestnik rossijskih universitetov. Matematika, Tome 27 (2022) no. 140, pp. 318-327. http://geodesic.mathdoc.fr/item/VTAMU_2022_27_140_a1/