A new firing paradigm for integrate and fire stochastic neuronal models
A new definition of firing time is given in the framework of Integrate and Fire neuronal models. The classical absorption condition at the threshold is relaxed and the firing time is defined as the first time the membrane potential process lies above a fixed depolarisation level for a sufficiently l...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016010 |
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| author | Roberta Sirovich Luisa Testa |
| author_facet | Roberta Sirovich Luisa Testa |
| author_sort | Roberta Sirovich |
| collection | DOAJ |
| description | A new definition of firing time is given in the framework of Integrate and Fire neuronal models. The classical absorption condition at the threshold is relaxed and the firing time is defined as the first time the membrane potential process lies above a fixed depolarisation level for a sufficiently long time. The mathematical properties of the new firing time are investigated both for the Perfect Integrator and the Leaky Integrator. In the latter case, a simulation study is presented to complete the analysis where analytical results are not yet achieved. |
| format | Article |
| id | doaj-art-1863ad9a7f9e46759980ee89f7defd91 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-1863ad9a7f9e46759980ee89f7defd912025-01-24T02:35:23ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-12-0113359761110.3934/mbe.2016010A new firing paradigm for integrate and fire stochastic neuronal modelsRoberta Sirovich0Luisa Testa1Department of Mathematics "G. Peano", University of Torino, Via Carlo Alberto 10, 10123 TorinoDepartment of Mathematics G. Peano, University of Torino, Via Carlo Alberto 10, 10123 - TorinoA new definition of firing time is given in the framework of Integrate and Fire neuronal models. The classical absorption condition at the threshold is relaxed and the firing time is defined as the first time the membrane potential process lies above a fixed depolarisation level for a sufficiently long time. The mathematical properties of the new firing time are investigated both for the Perfect Integrator and the Leaky Integrator. In the latter case, a simulation study is presented to complete the analysis where analytical results are not yet achieved.https://www.aimspress.com/article/doi/10.3934/mbe.2016010ito excursion theory.perfect integratorfirst passage timeleaky integratorfiring time |
| spellingShingle | Roberta Sirovich Luisa Testa A new firing paradigm for integrate and fire stochastic neuronal models Mathematical Biosciences and Engineering ito excursion theory. perfect integrator first passage time leaky integrator firing time |
| title | A new firing paradigm for integrate and fire stochastic neuronal models |
| title_full | A new firing paradigm for integrate and fire stochastic neuronal models |
| title_fullStr | A new firing paradigm for integrate and fire stochastic neuronal models |
| title_full_unstemmed | A new firing paradigm for integrate and fire stochastic neuronal models |
| title_short | A new firing paradigm for integrate and fire stochastic neuronal models |
| title_sort | new firing paradigm for integrate and fire stochastic neuronal models |
| topic | ito excursion theory. perfect integrator first passage time leaky integrator firing time |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016010 |
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