Email this article 
DYNAMIC SELF-ORGANIZATION IN NEURAL NETWORKS SYSTEMS
- Authors: Glyzin S.D1, Kolesov A.Y1, Fedulov D.D1
-
Affiliations:
- P.G. Demidov Yaroslavl State University, Center for Integrated Systems
- Issue: Vol 65, No 4 (2025)
- Pages: 574–589
- Section: Computer science
- URL: https://journals.rcsi.science/0044-4669/article/view/295431
- DOI: https://doi.org/10.31857/S0044466925040124
- EDN: https://elibrary.ru/IEEVOG
- ID: 295431
Cite item
Open Access
Access granted
Subscription Access
Abstract
The introduced concept of dynamic self-organization consists in the following. Suppose that there is a set of free (non-interacting) neurons, each of which is at rest or not capable of vibrational electrical activity at all. Then, being connected in a certain way in a network, these neurons can begin to generate electrical impulses. The feasibility of this phenomenon is illustrated by the example of one mathematical model, which is a certain nonlinear boundary value problem of hyperbolic type. A combination of analytical and numerical methods is used to study the attractors of the boundary value problem under consideration.
About the authors
S. D Glyzin
P.G. Demidov Yaroslavl State University, Center for Integrated Systems
Email: glyzin@uniyar.ac.ru
Yaroslavl, Russia
A. Y Kolesov
P.G. Demidov Yaroslavl State University, Center for Integrated Systems
Email: andkolesov@mail.ru
Yaroslavl, Russia
D. D Fedulov
P.G. Demidov Yaroslavl State University, Center for Integrated Systems
Email: mr.fedulow@yandex.ru
Yaroslavl, Russia
References
- Hodgkin A.L., Huxley A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve // J. Physiol. 1952. V. 117. P. 500–544.
- FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane // Biophys. J. 1961. V. 1. P. 445–466.
- Nagumo J., Arimoto S., Yoshizawa S. An active pulse transmission line simulating nerve axon // Proc. IRE. 1962. V. 50. P. 2061–2070.
- Колесов А.Ю., Розов Н.Х. Инвариантные торы нелинейных волновых уравнений. М.: Физматлит, 2004.
- Боголюбов Н.Н., Митропольский Ю.А. Асимптотические методы в теории нелинейных колебаний. М.: Наука, 1974.
- Колесов А.Ю., Розов Н.Х. Явление буферности и хаос в кольцевых цепочках однонаправленно связанных генераторов // Докл. АН. 2014. Т. 457. № 3. С. 278–281.
- Frederickson P., Kaplan J., Yorke J. The Lyapunov dimension of strange attractors // J. Different. Equat. 1983. V. 49. № 2. P. 185–207.
- Глызин С.Д., Колесов А.Ю., Розов Н.Х. Конечномерные модели диффузионного хаоса // Ж. вычисл. матем. и матем. физ. 2010. Т. 50. № 5. С. 860–875.
Supplementary files
