STATIONARY LOCALIZED ACTIVITY STRUCTURES IN TWO-DIMENSIONAL ENSEMBLE OF FITZHUGH–NAGUMO NEURONS WITH OSCILLATORY THRESHOLD


Cite this article as:

Dmitrichev А. S., Nekorkin . I. STATIONARY LOCALIZED ACTIVITY STRUCTURES IN TWO-DIMENSIONAL ENSEMBLE OF FITZHUGH–NAGUMO NEURONS WITH OSCILLATORY THRESHOLD. Izvestiya VUZ, Applied Nonlinear Dynamics, 2008, vol. 16, iss. 3, pp. 71-87 DOI: 10.18500/0869-6632-2008-16-3-71-87


We present the analysis of spatiotemporal dynamics of two-dimensional ensemble of electrically coupled FitzHugh–Nagumo neurons with oscillatory threshold. We show that in this system spatially localized activity structures can be formed. Such structures propagate through the system without changing their shape and velocity. We demonstrate that there exist two types of the structures: single and bound states. General characteristics of localized structures such as regions of existence, geometrical sizes and velocity are investigated. We also study structures interaction and give explanation for their existence and stability in terms of trajectories in associating with the ensemble multidimensional phase space.

DOI: 
10.18500/0869-6632-2008-16-3-71-87
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BibTeX

@article{Дмитричев -IzvVUZ_AND-16-3-71,
author = {А. S. Dmitrichev and Vladimir I. Nekorkin},
title = {STATIONARY LOCALIZED ACTIVITY STRUCTURES IN TWO-DIMENSIONAL ENSEMBLE OF FITZHUGH–NAGUMO NEURONS WITH OSCILLATORY THRESHOLD},
year = {2008},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {16},number = {3},
url = {http://andjournal.sgu.ru/en/articles/stationary-localized-activity-structures-in-two-dimensional-ensemble-of-fitzhugh-nagumo},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2008-16-3-71-87},pages = {71--87},issn = {0869-6632},
keywords = {СТАЦИОНАРНЫЕ ЛОКАЛИЗОВАННЫЕ СТРУКТУРЫ АКТИВНОСТИ В ДВУМЕРНОМ АНСАМБЛЕ МОДЕЛЬНЫХ НЕЙРОНОВ ФИТЦХЬЮ–НАГУМО С ОСЦИЛЛЯТОРНЫМ ПОРОГОМ},
abstract = {We present the analysis of spatiotemporal dynamics of two-dimensional ensemble of electrically coupled FitzHugh–Nagumo neurons with oscillatory threshold. We show that in this system spatially localized activity structures can be formed. Such structures propagate through the system without changing their shape and velocity. We demonstrate that there exist two types of the structures: single and bound states. General characteristics of localized structures such as regions of existence, geometrical sizes and velocity are investigated. We also study structures interaction and give explanation for their existence and stability in terms of trajectories in associating with the ensemble multidimensional phase space. }}