Long-time Behaviour of the Non-autonomous Stochastic FitzHugh-Nagumo Systems on Thin Domains
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912140524257280 |
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| author | Li, Dingshi Li, Ran Zeng, Tianhao |
| author_facet | Li, Dingshi Li, Ran Zeng, Tianhao |
| contents | We study the long-time behavior of non-autonomous stochastic FitzHugh-Nagumo systems on thin domains. As the $(n+ 1)$-dimensional thin domains collapses onto an n-dimensional domain, an n-dimensional limiting FitzHugh-Nagumo system is derived. This n-dimensional limiting system encodes the defining geometry of the $(n+1)$-dimensional system. To justify this limiting process, we show that the pullback measure attractors of the FitzHugh-Nagumo systems on thin domains are upper semi-continuous as the height of thin direction tends to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01205 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long-time Behaviour of the Non-autonomous Stochastic FitzHugh-Nagumo Systems on Thin Domains Li, Dingshi Li, Ran Zeng, Tianhao Dynamical Systems We study the long-time behavior of non-autonomous stochastic FitzHugh-Nagumo systems on thin domains. As the $(n+ 1)$-dimensional thin domains collapses onto an n-dimensional domain, an n-dimensional limiting FitzHugh-Nagumo system is derived. This n-dimensional limiting system encodes the defining geometry of the $(n+1)$-dimensional system. To justify this limiting process, we show that the pullback measure attractors of the FitzHugh-Nagumo systems on thin domains are upper semi-continuous as the height of thin direction tends to zero. |
| title | Long-time Behaviour of the Non-autonomous Stochastic FitzHugh-Nagumo Systems on Thin Domains |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2412.01205 |