Elimination of spiral waves in a two-dimensional Hindmarsh–Rose neural network under long-range interaction effect and frequency excitation

A. S. Etémé, C. B. Tabi, A. Mohamadou, T. C. Kofané

Research output: Contribution to journalArticle

Abstract

The elimination of spiral waves is numerically studied in a network of Hindmarsh–Rose neurons in presence of long-range diffusive interactions and external frequency excitations. Some features of membrane potential, including time series, spatiotemporal and spatial diagrams are discussed. It is found that at low frequency excitations, weak and strong long-range couplings sustain target wave propagation and spiral wave formation. However, ultra-long-range connections fully suppress such patterns, especially in the case of a Kac–Baker-like long-range coupling. In addition, increase in the excitation frequency supports the transition from stable robust spiral waves to spiral turbulence at weak or strong long-range connections. The interplay between hyper-high-frequency excitation and Kac–Baker-like long-range interaction completely eliminates spiral waves and only regenerates target wave propagation. Our results suggest that both frequency excitation regimes and long-range interaction may efficiently regulate the electrical activity of thalamus neurons and effectively prevent some brain disorders such as epileptic seizures.

Original languageEnglish
Article number122037
JournalPhysica A: Statistical Mechanics and its Applications
Volume533
DOIs
Publication statusPublished - Nov 1 2019

Fingerprint

Spiral Wave
Interaction Effects
Long-range Interactions
Elimination
elimination
Excitation
Neural Networks
Range of data
excitation
neurons
Wave Propagation
interactions
Neuron
wave propagation
thalamus
seizures
Membrane Potential
Target
brain
Low Frequency

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

@article{c2c173f1fe2240f49005cf17a5363232,
title = "Elimination of spiral waves in a two-dimensional Hindmarsh–Rose neural network under long-range interaction effect and frequency excitation",
abstract = "The elimination of spiral waves is numerically studied in a network of Hindmarsh–Rose neurons in presence of long-range diffusive interactions and external frequency excitations. Some features of membrane potential, including time series, spatiotemporal and spatial diagrams are discussed. It is found that at low frequency excitations, weak and strong long-range couplings sustain target wave propagation and spiral wave formation. However, ultra-long-range connections fully suppress such patterns, especially in the case of a Kac–Baker-like long-range coupling. In addition, increase in the excitation frequency supports the transition from stable robust spiral waves to spiral turbulence at weak or strong long-range connections. The interplay between hyper-high-frequency excitation and Kac–Baker-like long-range interaction completely eliminates spiral waves and only regenerates target wave propagation. Our results suggest that both frequency excitation regimes and long-range interaction may efficiently regulate the electrical activity of thalamus neurons and effectively prevent some brain disorders such as epileptic seizures.",
author = "Et{\'e}m{\'e}, {A. S.} and Tabi, {C. B.} and A. Mohamadou and Kofan{\'e}, {T. C.}",
year = "2019",
month = "11",
day = "1",
doi = "10.1016/j.physa.2019.122037",
language = "English",
volume = "533",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",

}

TY - JOUR

T1 - Elimination of spiral waves in a two-dimensional Hindmarsh–Rose neural network under long-range interaction effect and frequency excitation

AU - Etémé, A. S.

AU - Tabi, C. B.

AU - Mohamadou, A.

AU - Kofané, T. C.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - The elimination of spiral waves is numerically studied in a network of Hindmarsh–Rose neurons in presence of long-range diffusive interactions and external frequency excitations. Some features of membrane potential, including time series, spatiotemporal and spatial diagrams are discussed. It is found that at low frequency excitations, weak and strong long-range couplings sustain target wave propagation and spiral wave formation. However, ultra-long-range connections fully suppress such patterns, especially in the case of a Kac–Baker-like long-range coupling. In addition, increase in the excitation frequency supports the transition from stable robust spiral waves to spiral turbulence at weak or strong long-range connections. The interplay between hyper-high-frequency excitation and Kac–Baker-like long-range interaction completely eliminates spiral waves and only regenerates target wave propagation. Our results suggest that both frequency excitation regimes and long-range interaction may efficiently regulate the electrical activity of thalamus neurons and effectively prevent some brain disorders such as epileptic seizures.

AB - The elimination of spiral waves is numerically studied in a network of Hindmarsh–Rose neurons in presence of long-range diffusive interactions and external frequency excitations. Some features of membrane potential, including time series, spatiotemporal and spatial diagrams are discussed. It is found that at low frequency excitations, weak and strong long-range couplings sustain target wave propagation and spiral wave formation. However, ultra-long-range connections fully suppress such patterns, especially in the case of a Kac–Baker-like long-range coupling. In addition, increase in the excitation frequency supports the transition from stable robust spiral waves to spiral turbulence at weak or strong long-range connections. The interplay between hyper-high-frequency excitation and Kac–Baker-like long-range interaction completely eliminates spiral waves and only regenerates target wave propagation. Our results suggest that both frequency excitation regimes and long-range interaction may efficiently regulate the electrical activity of thalamus neurons and effectively prevent some brain disorders such as epileptic seizures.

UR - http://www.scopus.com/inward/record.url?scp=85069546218&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069546218&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2019.122037

DO - 10.1016/j.physa.2019.122037

M3 - Article

VL - 533

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

M1 - 122037

ER -