The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters

This research presents an adaptive synchronization approach crafted to facilitate exact lag synchronization between a pair of unidirectionally linked Hindmarsh-Rose (HR) neurons, taking into account both explicit propagation delays and the existence of uncertain parameters. The precise condition for...

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Main Authors: Bin Zhen, Ya-Lan Li, Li-Jun Pei, Li-Jun Ouyang
Format: Article
Language:English
Published: AIMS Press 2024-10-01
Series:Electronic Research Archive
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Online Access:https://www.aimspress.com/article/doi/10.3934/era.2024257
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author Bin Zhen
Ya-Lan Li
Li-Jun Pei
Li-Jun Ouyang
author_facet Bin Zhen
Ya-Lan Li
Li-Jun Pei
Li-Jun Ouyang
author_sort Bin Zhen
collection DOAJ
description This research presents an adaptive synchronization approach crafted to facilitate exact lag synchronization between a pair of unidirectionally linked Hindmarsh-Rose (HR) neurons, taking into account both explicit propagation delays and the existence of uncertain parameters. The precise condition for lag synchronization is deduced analytically, utilizing the Laplace transform and convolution theorem, alongside the iterative approach within the framework of Volterra integral equations theory. The established criterion guarantees robust stability irrespective of the propagation delay's magnitude, facilitating the realization of approximate lag and anticipating synchronization in a pair of HR neurons. The approximate synchronizations are realized in the absence of direct time-delay coupling, with the Taylor series expansion serving as an alternative to the precise time-delay component. Numerical simulations are executed to validate the effectiveness of the suggested approximate synchronization approach. The research demonstrates that employing the current state of an HR neuron, despite having uncertain parameters, enables the accurate prediction of future states and the reconstruction of past states. This study provides a novel perspective for comprehending neural processes and the advantageous attributes inherent in nonlinear and chaotic systems.
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institution Kabale University
issn 2688-1594
language English
publishDate 2024-10-01
publisher AIMS Press
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series Electronic Research Archive
spelling doaj-art-16bfa96e414942259d4bd854fb7570632025-01-23T07:52:52ZengAIMS PressElectronic Research Archive2688-15942024-10-0132105557557610.3934/era.2024257The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parametersBin Zhen0Ya-Lan Li1Li-Jun Pei2Li-Jun Ouyang3School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, ChinaSchool of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, ChinaThis research presents an adaptive synchronization approach crafted to facilitate exact lag synchronization between a pair of unidirectionally linked Hindmarsh-Rose (HR) neurons, taking into account both explicit propagation delays and the existence of uncertain parameters. The precise condition for lag synchronization is deduced analytically, utilizing the Laplace transform and convolution theorem, alongside the iterative approach within the framework of Volterra integral equations theory. The established criterion guarantees robust stability irrespective of the propagation delay's magnitude, facilitating the realization of approximate lag and anticipating synchronization in a pair of HR neurons. The approximate synchronizations are realized in the absence of direct time-delay coupling, with the Taylor series expansion serving as an alternative to the precise time-delay component. Numerical simulations are executed to validate the effectiveness of the suggested approximate synchronization approach. The research demonstrates that employing the current state of an HR neuron, despite having uncertain parameters, enables the accurate prediction of future states and the reconstruction of past states. This study provides a novel perspective for comprehending neural processes and the advantageous attributes inherent in nonlinear and chaotic systems.https://www.aimspress.com/article/doi/10.3934/era.2024257lag synchronizationanticipating synchronizationhindmarsh-rose neuronvolterra integral equations
spellingShingle Bin Zhen
Ya-Lan Li
Li-Jun Pei
Li-Jun Ouyang
The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters
Electronic Research Archive
lag synchronization
anticipating synchronization
hindmarsh-rose neuron
volterra integral equations
title The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters
title_full The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters
title_fullStr The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters
title_full_unstemmed The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters
title_short The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters
title_sort approximate lag and anticipating synchronization between two unidirectionally coupled hindmarsh rose neurons with uncertain parameters
topic lag synchronization
anticipating synchronization
hindmarsh-rose neuron
volterra integral equations
url https://www.aimspress.com/article/doi/10.3934/era.2024257
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