Two-frequency self-oscillations in a FitzHugh–Nagumo neural network
- Authors: Glyzin S.D.1, Kolesov A.Y.1, Rozov N.K.2
-
Affiliations:
- Faculty of Mathematics
- Faculty of Mechanics and Mathematics
- Issue: Vol 57, No 1 (2017)
- Pages: 106-121
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/178874
- DOI: https://doi.org/10.1134/S0965542517010067
- ID: 178874
Cite item
Abstract
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.
About the authors
S. D. Glyzin
Faculty of Mathematics
Author for correspondence.
Email: glyzin@uniyar.ac.ru
Russian Federation, Yaroslavl, 150000
A. Yu. Kolesov
Faculty of Mathematics
Email: fpo.mgu@mail.ru
Russian Federation, Yaroslavl, 150000
N. Kh. Rozov
Faculty of Mechanics and Mathematics
Author for correspondence.
Email: fpo.mgu@mail.ru
Russian Federation, Moscow, 119991
Supplementary files
