On a Method of Mathematical Modeling of Electrical Synapses

We introduce a new mathematical model of a neural network with electrical connections. The model is a singularly perturbed system of delay differential–difference equations. Some methods for studying the existence and stability of periodic relaxation motions in this system are presented. In the case...

Full description

Saved in:
Bibliographic Details
Published inDifferential equations Vol. 58; no. 7; pp. 853 - 868
Main Authors Glyzin, S. D., Kolesov, A. Yu
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2022
Springer
Springer Nature B.V
Subjects
Difference and Functional Equations
Difference equations
Differential equations
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Motion stability
Neural networks
Ordinary Differential Equations
Partial Differential Equations
Synapses
Online AccessGet full text

Cover

More Information
Summary:We introduce a new mathematical model of a neural network with electrical connections. The model is a singularly perturbed system of delay differential–difference equations. Some methods for studying the existence and stability of periodic relaxation motions in this system are presented. In the case of diffusion and symmetric fully connected neural networks, we establish that the well-known buffering phenomenon can be realized in the corresponding mathematical models.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266122070011