Open AccessNonclassical relaxation oscillations in neurodynamics
Author(s) -
С. Д. Глызин,
A. Yu. Kolesov,
Н. Х. Розов
Publication year - 2016
Publication title -
automatic control and computer sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.299
H-Index - 17
eISSN - 1558-108X
pISSN - 0146-4116
DOI - 10.3103/s0146411616070063
Subject(s) - ordinary differential equation , relaxation oscillator , relaxation (psychology) , traveling wave , variable (mathematics) , component (thermodynamics) , function (biology) , stability (learning theory) , stability theory , chain (unit) , physics , computer science , differential equation , mathematical analysis , mathematics , control theory (sociology) , nonlinear system , neuroscience , quantum mechanics , biology , control (management) , voltage , voltage controlled oscillator , evolutionary biology , machine learning , artificial intelligence
A modification of the well-known FitzHugh–Nagumo model from neuroscience has been proposed. This model is a singularly perturbed system of ordinary differential equations with a fast variable and a slow variable. The existence and stability of a nonclassical relaxation cycle in this system have been studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a δ-like function. A one-dimensional circle of unidirectionally coupled neurons has been considered. The existence of an arbitrarily large number of traveling waves for this chain has been shown. In order to illustrate the increase in the number of stable traveling waves, numerical methods were involved.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom