Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps

Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of t...

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Autores principales:	Mahtab Mehrabbeik, Fatemeh Parastesh, Janarthanan Ramadoss, Karthikeyan Rajagopal, Hamidreza Namazi, Sajad Jafari
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	synchronization chimera state memristor m-rulkov map neuronal network Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e6296307f39845409bd7c543d7c612ee
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spelling	oai:doaj.org-article:e6296307f39845409bd7c543d7c612ee2021-11-29T06:13:56ZSynchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps10.3934/mbe.20214621551-0018https://doaj.org/article/e6296307f39845409bd7c543d7c612ee2021-10-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021462?viewType=HTMLhttps://doaj.org/toc/1551-0018Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.Mahtab Mehrabbeik Fatemeh ParasteshJanarthanan RamadossKarthikeyan RajagopalHamidreza Namazi Sajad Jafari AIMS Pressarticlesynchronizationchimera statememristorm-rulkov mapneuronal networkBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 6, Pp 9394-9409 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	synchronization chimera state memristor m-rulkov map neuronal network Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	synchronization chimera state memristor m-rulkov map neuronal network Biotechnology TP248.13-248.65 Mathematics QA1-939 Mahtab Mehrabbeik Fatemeh Parastesh Janarthanan Ramadoss Karthikeyan Rajagopal Hamidreza Namazi Sajad Jafari Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps
description	Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.
format	article
author	Mahtab Mehrabbeik Fatemeh Parastesh Janarthanan Ramadoss Karthikeyan Rajagopal Hamidreza Namazi Sajad Jafari
author_facet	Mahtab Mehrabbeik Fatemeh Parastesh Janarthanan Ramadoss Karthikeyan Rajagopal Hamidreza Namazi Sajad Jafari
author_sort	Mahtab Mehrabbeik
title	Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps
title_short	Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps
title_full	Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps
title_fullStr	Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps
title_full_unstemmed	Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps
title_sort	synchronization and chimera states in the network of electrochemically coupled memristive rulkov neuron maps
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/e6296307f39845409bd7c543d7c612ee
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Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps

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