Long-range interaction effects on coupled excitable nodes: traveling waves and chimera state
In this paper, analytical and numerical studies of the influence of the long-range interaction parameter on the excitability threshold in a ring of FitzHugh-Nagumo (FHN) system are investigated. The long-range interaction is introduced to the network to model regulation of the Gap junctions or hemic...
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| Language: | English |
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Elsevier
2021-05-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844021011294 |
| _version_ | 1819005212422045696 |
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| author | Guy Blondeau Soh Robert Tchitnga Paul Woafo |
| author_facet | Guy Blondeau Soh Robert Tchitnga Paul Woafo |
| author_sort | Guy Blondeau Soh |
| collection | DOAJ |
| description | In this paper, analytical and numerical studies of the influence of the long-range interaction parameter on the excitability threshold in a ring of FitzHugh-Nagumo (FHN) system are investigated. The long-range interaction is introduced to the network to model regulation of the Gap junctions or hemichannels activity at the connexins level, which provides links between pre-synaptic and post-synaptic neurons. Results show that the long-range coupling enhances the range of the threshold parameter. We also investigate the long-range effects on the network dynamics, which induces enlargement of the oscillatory zone before the excitable regime. When considering bidirectional coupling, the long-range interaction induces traveling patterns such as traveling waves, while when considering unidirectional coupling, the long-range interaction induces multi-chimera states. We also studied the difference between the dynamics of coupled oscillators and coupled excitable neurons. We found that, for the coupled system, the oscillation period decreases with the increasing of the coupling parameter. For the same values of the coupling parameter, the oscillation period of the Oscillatory dynamics is greater than the oscillation period of the excitable dynamics. The analytical approximation shows good agreement with the numerical results. |
| first_indexed | 2024-12-20T23:49:12Z |
| format | Article |
| id | doaj.art-1ff8f94a88fb452da320f41eda50faae |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-12-20T23:49:12Z |
| publishDate | 2021-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-1ff8f94a88fb452da320f41eda50faae2022-12-21T19:22:52ZengElsevierHeliyon2405-84402021-05-0175e07026Long-range interaction effects on coupled excitable nodes: traveling waves and chimera stateGuy Blondeau Soh0Robert Tchitnga1Paul Woafo2Laboratory of Electronics, Automation and Signal Processing, Faculty of Science, Department of Physics, University of Dschang, P.O. Box 67, Dschang, CameroonLaboratory of Electronics, Automation and Signal Processing, Faculty of Science, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon; Institute of Surface Chemistry and Catalysis, University of Ulm, Albert-Einstein-Allee 47, 89081 Ulm, Germany; Corresponding author at: Laboratory of Electronics, Automation and Signal Processing, Faculty of Science, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon.Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, CameroonIn this paper, analytical and numerical studies of the influence of the long-range interaction parameter on the excitability threshold in a ring of FitzHugh-Nagumo (FHN) system are investigated. The long-range interaction is introduced to the network to model regulation of the Gap junctions or hemichannels activity at the connexins level, which provides links between pre-synaptic and post-synaptic neurons. Results show that the long-range coupling enhances the range of the threshold parameter. We also investigate the long-range effects on the network dynamics, which induces enlargement of the oscillatory zone before the excitable regime. When considering bidirectional coupling, the long-range interaction induces traveling patterns such as traveling waves, while when considering unidirectional coupling, the long-range interaction induces multi-chimera states. We also studied the difference between the dynamics of coupled oscillators and coupled excitable neurons. We found that, for the coupled system, the oscillation period decreases with the increasing of the coupling parameter. For the same values of the coupling parameter, the oscillation period of the Oscillatory dynamics is greater than the oscillation period of the excitable dynamics. The analytical approximation shows good agreement with the numerical results.http://www.sciencedirect.com/science/article/pii/S2405844021011294Traveling wavesMulti-chimera stateExcitable behaviorElectrical synapseLong-range interaction |
| spellingShingle | Guy Blondeau Soh Robert Tchitnga Paul Woafo Long-range interaction effects on coupled excitable nodes: traveling waves and chimera state Heliyon Traveling waves Multi-chimera state Excitable behavior Electrical synapse Long-range interaction |
| title | Long-range interaction effects on coupled excitable nodes: traveling waves and chimera state |
| title_full | Long-range interaction effects on coupled excitable nodes: traveling waves and chimera state |
| title_fullStr | Long-range interaction effects on coupled excitable nodes: traveling waves and chimera state |
| title_full_unstemmed | Long-range interaction effects on coupled excitable nodes: traveling waves and chimera state |
| title_short | Long-range interaction effects on coupled excitable nodes: traveling waves and chimera state |
| title_sort | long range interaction effects on coupled excitable nodes traveling waves and chimera state |
| topic | Traveling waves Multi-chimera state Excitable behavior Electrical synapse Long-range interaction |
| url | http://www.sciencedirect.com/science/article/pii/S2405844021011294 |
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