A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866914961532387328 |
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| author | Cormier, Quentin |
| author_facet | Cormier, Quentin |
| contents | We investigate a stochastic network composed of Integrate-and-Fire spiking neurons, focusing on its mean-field asymptotics. We consider an invariant probability measure of the McKean-Vlasov equation and establish an explicit sufficient condition to ensure the local stability of this invariant distribution. Furthermore, we prove a conjecture proposed initially by J. Touboul and P. Robert regarding the bistable nature of a specific instance of this neuronal model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_08649 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions Cormier, Quentin Probability Analysis of PDEs 60H10 (Primary) 60K35, 45D05, 37A30 (Secondary) We investigate a stochastic network composed of Integrate-and-Fire spiking neurons, focusing on its mean-field asymptotics. We consider an invariant probability measure of the McKean-Vlasov equation and establish an explicit sufficient condition to ensure the local stability of this invariant distribution. Furthermore, we prove a conjecture proposed initially by J. Touboul and P. Robert regarding the bistable nature of a specific instance of this neuronal model. |
| title | A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions |
| topic | Probability Analysis of PDEs 60H10 (Primary) 60K35, 45D05, 37A30 (Secondary) |
| url | https://arxiv.org/abs/2002.08649 |