A feedback control method for the stabilization of a nonlinear diffusion system on the graph
In this paper, we consider the internal stabilization problems of FitzHugh–Nagumo (FHN) systems on the locally finite connected weighted graphs, which describe the process of signal transmission across axons in neurobiology. We will establish the proper condition on the weighted Dirichlet–Laplace op...
| Main Authors: | , , |
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| Format: | Journal Article |
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Institute of Physics Publishing Ltd.
2014
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/43432 |
| _version_ | 1848756690129780736 |
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| author | Yu, X. Xu, C. Lin, Qun |
| author_facet | Yu, X. Xu, C. Lin, Qun |
| author_sort | Yu, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider the internal stabilization problems of FitzHugh–Nagumo (FHN) systems on the locally finite connected weighted graphs, which describe the process of signal transmission across axons in neurobiology. We will establish the proper condition on the weighted Dirichlet–Laplace operator on a graph such that the nonlinear FHN system can be stabilized exponentially and globally only using internal actuation over a sub-domain with a linear feedback form. |
| first_indexed | 2025-11-14T09:16:12Z |
| format | Journal Article |
| id | curtin-20.500.11937-43432 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:16:12Z |
| publishDate | 2014 |
| publisher | Institute of Physics Publishing Ltd. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-434322017-09-13T14:01:54Z A feedback control method for the stabilization of a nonlinear diffusion system on the graph Yu, X. Xu, C. Lin, Qun Mathematical physics Statistical physics and nonlinear systems In this paper, we consider the internal stabilization problems of FitzHugh–Nagumo (FHN) systems on the locally finite connected weighted graphs, which describe the process of signal transmission across axons in neurobiology. We will establish the proper condition on the weighted Dirichlet–Laplace operator on a graph such that the nonlinear FHN system can be stabilized exponentially and globally only using internal actuation over a sub-domain with a linear feedback form. 2014 Journal Article http://hdl.handle.net/20.500.11937/43432 10.1088/1674-1056/23/8/080206 Institute of Physics Publishing Ltd. restricted |
| spellingShingle | Mathematical physics Statistical physics and nonlinear systems Yu, X. Xu, C. Lin, Qun A feedback control method for the stabilization of a nonlinear diffusion system on the graph |
| title | A feedback control method for the stabilization of a nonlinear diffusion system on the graph |
| title_full | A feedback control method for the stabilization of a nonlinear diffusion system on the graph |
| title_fullStr | A feedback control method for the stabilization of a nonlinear diffusion system on the graph |
| title_full_unstemmed | A feedback control method for the stabilization of a nonlinear diffusion system on the graph |
| title_short | A feedback control method for the stabilization of a nonlinear diffusion system on the graph |
| title_sort | feedback control method for the stabilization of a nonlinear diffusion system on the graph |
| topic | Mathematical physics Statistical physics and nonlinear systems |
| url | http://hdl.handle.net/20.500.11937/43432 |