Robust synchronization of delayed chaotic FitzHugh-Nagumo neurons under external electrical stimulation
type: Item
instance of: scholarly article
title: Robust synchronization of delayed chaotic FitzHugh-Nagumo neurons under external electrical stimulation
zbMATH Open document ID: 1254.92015
DOI: 10.1155/2012/230980
author: Muhammad Rehan
author: Keum-Shik Hong
published in: Computational \& Mathematical Methods in Medicine
publication date: 2013-01-09T00:00:00Z
review text: Summary: Synchronization of chaotic neurons under external electrical stimulation (EES) is studied in order to understand information processing in the brain and to improve the methodologies employed in the treatment of cognitive diseases. This paper investigates the dynamics of uncertain coupled chaotic delayed FitzHugh-Nagumo (FHN) neurons under EES for incorporated parametric variations. A global nonlinear control law for synchronization of delayed neurons with known parameters is developed. Based on local and global Lipschitz conditions, knowledge of the bounds on the neuronal states, the Lyapunov-Krasovskii functional, and the \(L_2\) gain reduction, a less conservative local robust nonlinear control law is formulated to address the problem of robust asymptotic synchronization of delayed FHN neurons under parametric uncertainties. The proposed local control law guarantees both robust stability and robust performance and provides the \(L_2\) bound for uncertainty rejection in the synchronization error dynamics. Separate conditions for single-input and multiple-input control schemes for synchronization of a wide class of FHN systems are provided. The results of the proposed techniques are verified through numerical simulations.
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 92C05
Mathematics Subject Classification ID: 92B25
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 49N90
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92-08
zbMATH DE Number: 6123533
MaRDI profile type: Publication
Wikidata QID: Q36413529
full work available at URL: https://doi.org/10.1155/2012/230980
OpenAlex ID: W2130606505
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description: scientific article; zbMATH DE number 6123533