A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method
In this paper, an analytical criterion is proposed to investigate the synchronization between two Hindmarsh-Rose neurons with linear and nonlinear coupling functions based on the Laplace transform method. Different from previous works, the synchronization error system is expressed in its integral fo...
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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/10.1155/2021/6692132 |
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| author | Chunlin Su Bin Zhen Zigen Song |
| author_facet | Chunlin Su Bin Zhen Zigen Song |
| author_sort | Chunlin Su |
| collection | DOAJ |
| description | In this paper, an analytical criterion is proposed to investigate the synchronization between two Hindmarsh-Rose neurons with linear and nonlinear coupling functions based on the Laplace transform method. Different from previous works, the synchronization error system is expressed in its integral form, which is more convenient to analyze. The synchronization problem of two HR coupled neurons is ultimately converted into the stability problem of roots to a nonlinear algebraic equation. Then, an analytical criterion for synchronization between the two HR neurons can be given by using the Routh-Hurwitz criterion. Numerical simulations show that the synchronization criterion derived in this paper is valid, regardless of the periodic spikes or burst-spike chaotic behavior of the two HR neurons. Furthermore, the analytical results have almost the same accuracy as the conditional Lyapunov method. In addition, the calculation quantities always are small no matter the linear and nonlinear coupling functions, which show that the approach presented in this paper is easy to be developed to study synchronization between a large number of HR neurons. |
| format | Article |
| id | doaj-art-28a2d2345d4a4d2c80f1c665559f6059 |
| 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-28a2d2345d4a4d2c80f1c665559f60592025-02-03T05:52:39ZengWileyNeural Plasticity2090-59041687-54432021-01-01202110.1155/2021/66921326692132A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform MethodChunlin Su0Bin Zhen1Zigen Song2School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Information Technology, Shanghai Ocean University, Shanghai 201306, ChinaIn this paper, an analytical criterion is proposed to investigate the synchronization between two Hindmarsh-Rose neurons with linear and nonlinear coupling functions based on the Laplace transform method. Different from previous works, the synchronization error system is expressed in its integral form, which is more convenient to analyze. The synchronization problem of two HR coupled neurons is ultimately converted into the stability problem of roots to a nonlinear algebraic equation. Then, an analytical criterion for synchronization between the two HR neurons can be given by using the Routh-Hurwitz criterion. Numerical simulations show that the synchronization criterion derived in this paper is valid, regardless of the periodic spikes or burst-spike chaotic behavior of the two HR neurons. Furthermore, the analytical results have almost the same accuracy as the conditional Lyapunov method. In addition, the calculation quantities always are small no matter the linear and nonlinear coupling functions, which show that the approach presented in this paper is easy to be developed to study synchronization between a large number of HR neurons.http://dx.doi.org/10.1155/2021/6692132 |
| spellingShingle | Chunlin Su Bin Zhen Zigen Song A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method Neural Plasticity |
| title | A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method |
| title_full | A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method |
| title_fullStr | A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method |
| title_full_unstemmed | A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method |
| title_short | A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method |
| title_sort | synchronization criterion for two hindmarsh rose neurons with linear and nonlinear coupling functions based on the laplace transform method |
| url | http://dx.doi.org/10.1155/2021/6692132 |
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