Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control

Abstract Synchronization plays a significant role in information transfer and decision-making by neurons and brain neural networks. The development of control strategies for synchronizing a network of chaotic neurons with time delays, different direction-dependent coupling (unidirectional and bidire...

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Autores principales:	Malik Muhammad Ibrahim, Muhammad Ahmad Kamran, Malik Muhammad Naeem Mannan, Il Hyo Jung, Sangil Kim
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/eaa3bcc730a5466a879c938211305946
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spelling	oai:doaj.org-article:eaa3bcc730a5466a879c9382113059462021-12-02T10:54:06ZLag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control10.1038/s41598-021-82886-x2045-2322https://doaj.org/article/eaa3bcc730a5466a879c9382113059462021-02-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-82886-xhttps://doaj.org/toc/2045-2322Abstract Synchronization plays a significant role in information transfer and decision-making by neurons and brain neural networks. The development of control strategies for synchronizing a network of chaotic neurons with time delays, different direction-dependent coupling (unidirectional and bidirectional), and noise, particularly under external disturbances, is an essential and very challenging task. Researchers have extensively studied the synchronization mechanism of two coupled time-delayed neurons with bidirectional coupling and without incorporating the effect of noise, but not for time-delayed neural networks. To overcome these limitations, this study investigates the synchronization problem in a network of coupled FitzHugh–Nagumo (FHN) neurons by incorporating time delays, different direction-dependent coupling (unidirectional and bidirectional), noise, and ionic and external disturbances in the mathematical models. More specifically, this study investigates the synchronization of time-delayed unidirectional and bidirectional ring-structured FHN neuronal systems with and without external noise. Different gap junctions and delay parameters are used to incorporate time-delay dynamics in both neuronal networks. We also investigate the influence of the time delays between connected neurons on synchronization conditions. Further, to ensure the synchronization of the time-delayed FHN neuronal networks, different adaptive control laws are proposed for both unidirectional and bidirectional neuronal networks. In addition, necessary and sufficient conditions to achieve synchronization are provided by employing the Lyapunov stability theory. The results of numerical simulations conducted for different-sized multiple networks of time-delayed FHN neurons verify the effectiveness of the proposed adaptive control schemes.Malik Muhammad IbrahimMuhammad Ahmad KamranMalik Muhammad Naeem MannanIl Hyo JungSangil KimNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Malik Muhammad Ibrahim Muhammad Ahmad Kamran Malik Muhammad Naeem Mannan Il Hyo Jung Sangil Kim Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control
description	Abstract Synchronization plays a significant role in information transfer and decision-making by neurons and brain neural networks. The development of control strategies for synchronizing a network of chaotic neurons with time delays, different direction-dependent coupling (unidirectional and bidirectional), and noise, particularly under external disturbances, is an essential and very challenging task. Researchers have extensively studied the synchronization mechanism of two coupled time-delayed neurons with bidirectional coupling and without incorporating the effect of noise, but not for time-delayed neural networks. To overcome these limitations, this study investigates the synchronization problem in a network of coupled FitzHugh–Nagumo (FHN) neurons by incorporating time delays, different direction-dependent coupling (unidirectional and bidirectional), noise, and ionic and external disturbances in the mathematical models. More specifically, this study investigates the synchronization of time-delayed unidirectional and bidirectional ring-structured FHN neuronal systems with and without external noise. Different gap junctions and delay parameters are used to incorporate time-delay dynamics in both neuronal networks. We also investigate the influence of the time delays between connected neurons on synchronization conditions. Further, to ensure the synchronization of the time-delayed FHN neuronal networks, different adaptive control laws are proposed for both unidirectional and bidirectional neuronal networks. In addition, necessary and sufficient conditions to achieve synchronization are provided by employing the Lyapunov stability theory. The results of numerical simulations conducted for different-sized multiple networks of time-delayed FHN neurons verify the effectiveness of the proposed adaptive control schemes.
format	article
author	Malik Muhammad Ibrahim Muhammad Ahmad Kamran Malik Muhammad Naeem Mannan Il Hyo Jung Sangil Kim
author_facet	Malik Muhammad Ibrahim Muhammad Ahmad Kamran Malik Muhammad Naeem Mannan Il Hyo Jung Sangil Kim
author_sort	Malik Muhammad Ibrahim
title	Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control
title_short	Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control
title_full	Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control
title_fullStr	Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control
title_full_unstemmed	Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control
title_sort	lag synchronization of coupled time-delayed fitzhugh–nagumo neural networks via feedback control
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/eaa3bcc730a5466a879c938211305946
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Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control

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