The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method
The synchronization between two coupled FitzHugh-Nagumo (FHN) neurons with or without external current is studied by using the Laplace transform and the Adomian decomposition method. Different from other researches, the synchronization error system is expressed as sets of Volterra integral equations...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Neural Plasticity |
| Online Access: | http://dx.doi.org/10.1155/2021/6657835 |
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| author | Bin Zhen Zigen Song |
| author_facet | Bin Zhen Zigen Song |
| author_sort | Bin Zhen |
| collection | DOAJ |
| description | The synchronization between two coupled FitzHugh-Nagumo (FHN) neurons with or without external current is studied by using the Laplace transform and the Adomian decomposition method. Different from other researches, the synchronization error system is expressed as sets of Volterra integral equations based on the convolution theorem in the Laplace transform. Then, it is easy to analytically obtain the conditions that synchronization errors disappear based on the successive approximation method in integral equation theorem, the correctness of which is verified by numerical simulations. Furthermore, the synchronous dynamics of the two coupled FHN neurons also can be written in the form of Volterra integral equations, which is more convenient to analytically solve by using the Adomian decomposition method. It is found that the occurrence of synchronization between the two FHN neurons only depends on the coupling strength and is irrelevant to the external current. Only synchronous rest state in the two FHN neurons without external current can be achieved, while synchronous spikes appear if the external current is not zero. |
| format | Article |
| id | doaj-art-5c9ad1b1aa4a405aaac50ec5d89302fd |
| institution | Kabale University |
| issn | 2090-5904 1687-5443 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Neural Plasticity |
| spelling | doaj-art-5c9ad1b1aa4a405aaac50ec5d89302fd2025-02-03T01:29:20ZengWileyNeural Plasticity2090-59041687-54432021-01-01202110.1155/2021/66578356657835The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition MethodBin Zhen0Zigen Song1School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Information Technology, Shanghai Ocean University, Shanghai 201306, ChinaThe synchronization between two coupled FitzHugh-Nagumo (FHN) neurons with or without external current is studied by using the Laplace transform and the Adomian decomposition method. Different from other researches, the synchronization error system is expressed as sets of Volterra integral equations based on the convolution theorem in the Laplace transform. Then, it is easy to analytically obtain the conditions that synchronization errors disappear based on the successive approximation method in integral equation theorem, the correctness of which is verified by numerical simulations. Furthermore, the synchronous dynamics of the two coupled FHN neurons also can be written in the form of Volterra integral equations, which is more convenient to analytically solve by using the Adomian decomposition method. It is found that the occurrence of synchronization between the two FHN neurons only depends on the coupling strength and is irrelevant to the external current. Only synchronous rest state in the two FHN neurons without external current can be achieved, while synchronous spikes appear if the external current is not zero.http://dx.doi.org/10.1155/2021/6657835 |
| spellingShingle | Bin Zhen Zigen Song The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method Neural Plasticity |
| title | The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method |
| title_full | The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method |
| title_fullStr | The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method |
| title_full_unstemmed | The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method |
| title_short | The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method |
| title_sort | study for synchronization between two coupled fitzhugh nagumo neurons based on the laplace transform and the adomian decomposition method |
| url | http://dx.doi.org/10.1155/2021/6657835 |
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