The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radia...

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Autores principales:	Xin Yang, Guangjun Zhang, Xueren Li, Dong Wang
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	fractional-order neuronal model synchronization transition neuronal network electromagnetic radiation Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/d913cacc96ad4ba0ba6979cb45ee4e1b
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id	oai:doaj.org-article:d913cacc96ad4ba0ba6979cb45ee4e1b
record_format	dspace
institution	DOAJ
collection	DOAJ
language	EN
topic	fractional-order neuronal model synchronization transition neuronal network electromagnetic radiation Mathematics QA1-939
spellingShingle	fractional-order neuronal model synchronization transition neuronal network electromagnetic radiation Mathematics QA1-939 Xin Yang Guangjun Zhang Xueren Li Dong Wang The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation
description	Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>q</mi></semantics></math></inline-formula> and the feedback gain parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>. In addition, the fractional-order or the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>q</mi></semantics></math></inline-formula> or parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> of the electromagnetic radiation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>q</mi></semantics></math></inline-formula>, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>q</mi></semantics></math></inline-formula> can be summarized into three cases: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>></mo><mn>0.02</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>0.06</mn><mo><</mo><mi>β</mi><mo><</mo><mn>0.02</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo><</mo><mo>−</mo><mn>0.06</mn></mrow></semantics></math></inline-formula>. The influence rules and some interesting phenomena are investigated.
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	The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation
title_short	The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation
title_full	The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation
title_fullStr	The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation
title_full_unstemmed	The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation
title_sort	synchronization behaviors of coupled fractional-order neuronal networks under electromagnetic radiation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/d913cacc96ad4ba0ba6979cb45ee4e1b
work_keys_str_mv	AT xinyang thesynchronizationbehaviorsofcoupledfractionalorderneuronalnetworksunderelectromagneticradiation AT guangjunzhang thesynchronizationbehaviorsofcoupledfractionalorderneuronalnetworksunderelectromagneticradiation AT xuerenli thesynchronizationbehaviorsofcoupledfractionalorderneuronalnetworksunderelectromagneticradiation AT dongwang thesynchronizationbehaviorsofcoupledfractionalorderneuronalnetworksunderelectromagneticradiation AT xinyang synchronizationbehaviorsofcoupledfractionalorderneuronalnetworksunderelectromagneticradiation AT guangjunzhang synchronizationbehaviorsofcoupledfractionalorderneuronalnetworksunderelectromagneticradiation AT xuerenli synchronizationbehaviorsofcoupledfractionalorderneuronalnetworksunderelectromagneticradiation AT dongwang synchronizationbehaviorsofcoupledfractionalorderneuronalnetworksunderelectromagneticradiation
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spelling	oai:doaj.org-article:d913cacc96ad4ba0ba6979cb45ee4e1b2021-11-25T19:07:34ZThe Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation10.3390/sym131122042073-8994https://doaj.org/article/d913cacc96ad4ba0ba6979cb45ee4e1b2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2204https://doaj.org/toc/2073-8994Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>q</mi></semantics></math></inline-formula> and the feedback gain parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>. In addition, the fractional-order or the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>q</mi></semantics></math></inline-formula> or parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> of the electromagnetic radiation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>q</mi></semantics></math></inline-formula>, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>q</mi></semantics></math></inline-formula> can be summarized into three cases: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>></mo><mn>0.02</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>0.06</mn><mo><</mo><mi>β</mi><mo><</mo><mn>0.02</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo><</mo><mo>−</mo><mn>0.06</mn></mrow></semantics></math></inline-formula>. The influence rules and some interesting phenomena are investigated.Xin YangGuangjun ZhangXueren LiDong WangMDPI AGarticlefractional-order neuronal modelsynchronization transitionneuronal networkelectromagnetic radiationMathematicsQA1-939ENSymmetry, Vol 13, Iss 2204, p 2204 (2021)

The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation

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