Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order

It is important to investigate the firing activities of neurons, and previous experimental works have shown that fractional-order neuronal models depict the firing rate of neurons more verifiably. In this study, a modified fractional-order Hindmarsh–Rose neuronal model is proposed, and the dynamics...

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Autores principales:	Xin Yang, GuangJun Zhang, XueRen Li, Dong Wang
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi-Wiley 2021
Materias:	Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/9db9a9dd5cc443ac9803d8e28bd2050f
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spelling	oai:doaj.org-article:9db9a9dd5cc443ac9803d8e28bd2050f2021-11-22T01:11:19ZDiverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order1099-052610.1155/2021/8490695https://doaj.org/article/9db9a9dd5cc443ac9803d8e28bd2050f2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/8490695https://doaj.org/toc/1099-0526It is important to investigate the firing activities of neurons, and previous experimental works have shown that fractional-order neuronal models depict the firing rate of neurons more verifiably. In this study, a modified fractional-order Hindmarsh–Rose neuronal model is proposed, and the dynamics and firing activities are investigated. Some novel phenomenon can be found. First, by analyzing numerically and theoretically, the Hopf bifurcation is found to occur when the external direct current stimulus is chosen appropriately. The effects of fractional-order on the bifurcation are also studied. Second, when injecting a direct current stimulus, compared with the integer-order model, the system has more varying dynamic behaviors and firing pattern transitions. Under different external current stimulus, periodic firing patterns and chaotic firing patterns occur when fractional-order changes, but the regions of chaotic firing patterns are different. In other words, the transition mode of periodic firing and chaotic firing induced by fractional-order is different under different external current stimulus. The two-dimensional colored diagram of firing patterns is also investigated. Finally, when injecting periodic current stimulus, regular/irregular bursting, multiple spiking, regular\irregular square wave bursting, and mixed firing mods are found by setting the appropriate fractional-order, amplitude, and frequency of the external current stimulus. Some firing patterns cannot be found in integer-order models. When the amplitude is chosen at appropriate values, the region of frequency when the system displays the mixed firing modes decreases with increasing fractional-order.Xin YangGuangJun ZhangXueRen LiDong WangHindawi-WileyarticleElectronic computers. Computer scienceQA75.5-76.95ENComplexity, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Electronic computers. Computer science QA75.5-76.95
spellingShingle	Electronic computers. Computer science QA75.5-76.95 Xin Yang GuangJun Zhang XueRen Li Dong Wang Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order
description	It is important to investigate the firing activities of neurons, and previous experimental works have shown that fractional-order neuronal models depict the firing rate of neurons more verifiably. In this study, a modified fractional-order Hindmarsh–Rose neuronal model is proposed, and the dynamics and firing activities are investigated. Some novel phenomenon can be found. First, by analyzing numerically and theoretically, the Hopf bifurcation is found to occur when the external direct current stimulus is chosen appropriately. The effects of fractional-order on the bifurcation are also studied. Second, when injecting a direct current stimulus, compared with the integer-order model, the system has more varying dynamic behaviors and firing pattern transitions. Under different external current stimulus, periodic firing patterns and chaotic firing patterns occur when fractional-order changes, but the regions of chaotic firing patterns are different. In other words, the transition mode of periodic firing and chaotic firing induced by fractional-order is different under different external current stimulus. The two-dimensional colored diagram of firing patterns is also investigated. Finally, when injecting periodic current stimulus, regular/irregular bursting, multiple spiking, regular\irregular square wave bursting, and mixed firing mods are found by setting the appropriate fractional-order, amplitude, and frequency of the external current stimulus. Some firing patterns cannot be found in integer-order models. When the amplitude is chosen at appropriate values, the region of frequency when the system displays the mixed firing modes decreases with increasing fractional-order.
format	article
author	Xin Yang GuangJun Zhang XueRen Li Dong Wang
author_facet	Xin Yang GuangJun Zhang XueRen Li Dong Wang
author_sort	Xin Yang
title	Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order
title_short	Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order
title_full	Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order
title_fullStr	Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order
title_full_unstemmed	Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order
title_sort	diverse dynamic behaviors and firing activities of the modified fractional-order hindmarsh–rose neuronal model induced by fractional-order
publisher	Hindawi-Wiley
publishDate	2021
url	https://doaj.org/article/9db9a9dd5cc443ac9803d8e28bd2050f
work_keys_str_mv	AT xinyang diversedynamicbehaviorsandfiringactivitiesofthemodifiedfractionalorderhindmarshroseneuronalmodelinducedbyfractionalorder AT guangjunzhang diversedynamicbehaviorsandfiringactivitiesofthemodifiedfractionalorderhindmarshroseneuronalmodelinducedbyfractionalorder AT xuerenli diversedynamicbehaviorsandfiringactivitiesofthemodifiedfractionalorderhindmarshroseneuronalmodelinducedbyfractionalorder AT dongwang diversedynamicbehaviorsandfiringactivitiesofthemodifiedfractionalorderhindmarshroseneuronalmodelinducedbyfractionalorder
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Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order

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