Two-frequency self-oscillations in a FitzHugh–Nagumo neural network
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 1, pp. 94-110
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A new mathematical model of a one-dimensional array of FitzHugh–Nagumo neurons with resistive-inductive coupling between neighboring elements is proposed. The model relies on a chain of diffusively coupled three-dimensional systems of ordinary differential equations. It is shown that any finite number of coexisting stable invariant two-dimensional tori can be obtained in this chain by suitably increasing the number of its elements.
@article{ZVMMF_2017_57_1_a8,
author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
title = {Two-frequency self-oscillations in a {FitzHugh{\textendash}Nagumo} neural network},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {94--110},
publisher = {mathdoc},
volume = {57},
number = {1},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a8/}
}
TY - JOUR AU - S. D. Glyzin AU - A. Yu. Kolesov AU - N. Kh. Rozov TI - Two-frequency self-oscillations in a FitzHugh–Nagumo neural network JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2017 SP - 94 EP - 110 VL - 57 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a8/ LA - ru ID - ZVMMF_2017_57_1_a8 ER -
%0 Journal Article %A S. D. Glyzin %A A. Yu. Kolesov %A N. Kh. Rozov %T Two-frequency self-oscillations in a FitzHugh–Nagumo neural network %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2017 %P 94-110 %V 57 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a8/ %G ru %F ZVMMF_2017_57_1_a8
S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Two-frequency self-oscillations in a FitzHugh–Nagumo neural network. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 1, pp. 94-110. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a8/