Two-frequency self-oscillations in a FitzHugh–Nagumo neural network


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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

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