Global Identification of FitzHugh-Nagumo Equation via Deterministic Learning and Interpolation
Spiral wave is closely related to the occurrence of malignant ventricular arrhythmia. It is important and necessary to study the spiral wave dynamics to better analyze and control spiral waves. In this paper, the dynamics of FitzHugh-Nagumo(FHN) model is identified by using a novel method based on d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2019-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8786115/ |
| _version_ | 1818596704517095424 |
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| author | Xunde Dong Wenjie Si Cong Wang |
| author_facet | Xunde Dong Wenjie Si Cong Wang |
| author_sort | Xunde Dong |
| collection | DOAJ |
| description | Spiral wave is closely related to the occurrence of malignant ventricular arrhythmia. It is important and necessary to study the spiral wave dynamics to better analyze and control spiral waves. In this paper, the dynamics of FitzHugh-Nagumo(FHN) model is identified by using a novel method based on deterministic learning and interpolation method. The FHN model, which has been studied extensively in physical and mathematical science, is often used to study spiral waves. It is a distributed parameter (DPS) described by two coupled partial differential equations (PDEs). To identify the underlying system dynamics of the FHN model globally, we first transform the FHN model into a set of ordinary differential equations (ODEs) by applying the method of lines. Then, we identify the dynamics of the approximation system by employing deterministic learning. That is, the FHN dynamics on a set of spatial grid nodes is accurately identified. To achieve the global identification of the FHN model, the underlying system dynamics of the FHN model on any other spatial point is approximated via an algorithm based on the interpolation method. The effectiveness and feasibility of the proposed method are demonstrated theoretically and numerically. |
| first_indexed | 2024-12-16T11:36:08Z |
| format | Article |
| id | doaj.art-6141056f38904be8bc6dc177aae32b8d |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T11:36:08Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-6141056f38904be8bc6dc177aae32b8d2022-12-21T22:33:06ZengIEEEIEEE Access2169-35362019-01-01710733410734510.1109/ACCESS.2019.29327948786115Global Identification of FitzHugh-Nagumo Equation via Deterministic Learning and InterpolationXunde Dong0https://orcid.org/0000-0001-8688-2662Wenjie Si1Cong Wang2School of Automation Science and Engineering, South China University of Technology, Guangzhou, ChinaSchool of Electrical and Control Engineering, Henan University of Urban Construction, Pingdingshan, ChinaSchool of Automation Science and Engineering, South China University of Technology, Guangzhou, ChinaSpiral wave is closely related to the occurrence of malignant ventricular arrhythmia. It is important and necessary to study the spiral wave dynamics to better analyze and control spiral waves. In this paper, the dynamics of FitzHugh-Nagumo(FHN) model is identified by using a novel method based on deterministic learning and interpolation method. The FHN model, which has been studied extensively in physical and mathematical science, is often used to study spiral waves. It is a distributed parameter (DPS) described by two coupled partial differential equations (PDEs). To identify the underlying system dynamics of the FHN model globally, we first transform the FHN model into a set of ordinary differential equations (ODEs) by applying the method of lines. Then, we identify the dynamics of the approximation system by employing deterministic learning. That is, the FHN dynamics on a set of spatial grid nodes is accurately identified. To achieve the global identification of the FHN model, the underlying system dynamics of the FHN model on any other spatial point is approximated via an algorithm based on the interpolation method. The effectiveness and feasibility of the proposed method are demonstrated theoretically and numerically.https://ieeexplore.ieee.org/document/8786115/Dynamicssystem identificationradial basis function networksinterpolation |
| spellingShingle | Xunde Dong Wenjie Si Cong Wang Global Identification of FitzHugh-Nagumo Equation via Deterministic Learning and Interpolation IEEE Access Dynamics system identification radial basis function networks interpolation |
| title | Global Identification of FitzHugh-Nagumo Equation via Deterministic Learning and Interpolation |
| title_full | Global Identification of FitzHugh-Nagumo Equation via Deterministic Learning and Interpolation |
| title_fullStr | Global Identification of FitzHugh-Nagumo Equation via Deterministic Learning and Interpolation |
| title_full_unstemmed | Global Identification of FitzHugh-Nagumo Equation via Deterministic Learning and Interpolation |
| title_short | Global Identification of FitzHugh-Nagumo Equation via Deterministic Learning and Interpolation |
| title_sort | global identification of fitzhugh nagumo equation via deterministic learning and interpolation |
| topic | Dynamics system identification radial basis function networks interpolation |
| url | https://ieeexplore.ieee.org/document/8786115/ |
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