Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model
Neuron modelling helps to understand the brain behavior through the interaction between neurons, but its mechanism remains unclear. In this paper, the spatiotemporal patterns is investigated in a general networked Hindmarsh-Rose (HR) model. The stability of the network-organized system without delay...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-06-01
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| Series: | Frontiers in Physiology |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphys.2022.936982/full |
| _version_ | 1811238788796514304 |
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| author | Qianqian Zheng Jianwei Shen Rui Zhang Linan Guan Yong Xu |
| author_facet | Qianqian Zheng Jianwei Shen Rui Zhang Linan Guan Yong Xu |
| author_sort | Qianqian Zheng |
| collection | DOAJ |
| description | Neuron modelling helps to understand the brain behavior through the interaction between neurons, but its mechanism remains unclear. In this paper, the spatiotemporal patterns is investigated in a general networked Hindmarsh-Rose (HR) model. The stability of the network-organized system without delay is analyzed to show the effect of the network on Turing instability through the Hurwitz criterion, and the conditions of Turing instability are obtained. Once the analysis of the zero-delayed system is completed, the critical value of the delay is derived to illustrate the profound impact of the given network on the collected behaviors. It is found that the difference between the collected current and the outgoing current plays a crucial role in neuronal activity, which can be used to explain the generation mechanism of the short-term memory. Finally, the numerical simulation is presented to verify the proposed theoretical results. |
| first_indexed | 2024-04-12T12:48:16Z |
| format | Article |
| id | doaj.art-777ec443591a435591e46893fd52538a |
| institution | Directory Open Access Journal |
| issn | 1664-042X |
| language | English |
| last_indexed | 2024-04-12T12:48:16Z |
| publishDate | 2022-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physiology |
| spelling | doaj.art-777ec443591a435591e46893fd52538a2022-12-22T03:32:33ZengFrontiers Media S.A.Frontiers in Physiology1664-042X2022-06-011310.3389/fphys.2022.936982936982Spatiotemporal Patterns in a General Networked Hindmarsh-Rose ModelQianqian Zheng0Jianwei Shen1Rui Zhang2Linan Guan3Yong Xu4School of Science, Xuchang University, Xuchang, ChinaSchool of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, ChinaSchool of Mathematics, Northwest University, Xi’an, ChinaSchool of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, ChinaNeuron modelling helps to understand the brain behavior through the interaction between neurons, but its mechanism remains unclear. In this paper, the spatiotemporal patterns is investigated in a general networked Hindmarsh-Rose (HR) model. The stability of the network-organized system without delay is analyzed to show the effect of the network on Turing instability through the Hurwitz criterion, and the conditions of Turing instability are obtained. Once the analysis of the zero-delayed system is completed, the critical value of the delay is derived to illustrate the profound impact of the given network on the collected behaviors. It is found that the difference between the collected current and the outgoing current plays a crucial role in neuronal activity, which can be used to explain the generation mechanism of the short-term memory. Finally, the numerical simulation is presented to verify the proposed theoretical results.https://www.frontiersin.org/articles/10.3389/fphys.2022.936982/fullHR modelpattern formationnetworkmatrixturing instabilitydelay |
| spellingShingle | Qianqian Zheng Jianwei Shen Rui Zhang Linan Guan Yong Xu Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model Frontiers in Physiology HR model pattern formation network matrix turing instability delay |
| title | Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model |
| title_full | Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model |
| title_fullStr | Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model |
| title_full_unstemmed | Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model |
| title_short | Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model |
| title_sort | spatiotemporal patterns in a general networked hindmarsh rose model |
| topic | HR model pattern formation network matrix turing instability delay |
| url | https://www.frontiersin.org/articles/10.3389/fphys.2022.936982/full |
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