The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry
The neuron model with conductance-resistance symmetry was recently derived by Deng, which is similar to the Hodgkin-Huxley equation, referred to as CRS neuron model. In this paper, we will consider a 2-dimensional reduction model qualitatively similar to the FitzHugh-Nagumo equation. We first give t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023171?viewType=HTML |
| _version_ | 1797953977097125888 |
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| author | Feifei Cheng Ji Li Qing Yu |
| author_facet | Feifei Cheng Ji Li Qing Yu |
| author_sort | Feifei Cheng |
| collection | DOAJ |
| description | The neuron model with conductance-resistance symmetry was recently derived by Deng, which is similar to the Hodgkin-Huxley equation, referred to as CRS neuron model. In this paper, we will consider a 2-dimensional reduction model qualitatively similar to the FitzHugh-Nagumo equation. We first give the derivation of the CRS neuron model in propagating action potential. And then we prove the existence of solitary wave solution for the 2-dimensional reduced CRS neuron model by using phase diagram analysis. |
| first_indexed | 2024-04-10T23:10:28Z |
| format | Article |
| id | doaj.art-cd4a847f31b942c88453d25e9a9f15ba |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T23:10:28Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-cd4a847f31b942c88453d25e9a9f15ba2023-01-13T05:56:56ZengAIMS PressAIMS Mathematics2473-69882023-01-01823322333710.3934/math.2023171The existence of solitary wave solutions for the neuron model with conductance-resistance symmetryFeifei Cheng0Ji Li1Qing Yu21. Department of Mathematics and Physics, Henan University of Urban Construction, Pingdingshan, Henan 467036, China2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, ChinaThe neuron model with conductance-resistance symmetry was recently derived by Deng, which is similar to the Hodgkin-Huxley equation, referred to as CRS neuron model. In this paper, we will consider a 2-dimensional reduction model qualitatively similar to the FitzHugh-Nagumo equation. We first give the derivation of the CRS neuron model in propagating action potential. And then we prove the existence of solitary wave solution for the 2-dimensional reduced CRS neuron model by using phase diagram analysis.https://www.aimspress.com/article/doi/10.3934/math.2023171?viewType=HTMLneuron modeltraveling wavessolitary wave solutionshomoclinic orbitsfitzhugh-nagumo equation |
| spellingShingle | Feifei Cheng Ji Li Qing Yu The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry AIMS Mathematics neuron model traveling waves solitary wave solutions homoclinic orbits fitzhugh-nagumo equation |
| title | The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry |
| title_full | The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry |
| title_fullStr | The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry |
| title_full_unstemmed | The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry |
| title_short | The existence of solitary wave solutions for the neuron model with conductance-resistance symmetry |
| title_sort | existence of solitary wave solutions for the neuron model with conductance resistance symmetry |
| topic | neuron model traveling waves solitary wave solutions homoclinic orbits fitzhugh-nagumo equation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023171?viewType=HTML |
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