On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model
An Ornstein-Uhlenbeck diffusion process is considered as a model for the membrane potential activity of a single neuron. We assume that the neuron is subject to a sequence of inhibitory and excitatory post-synaptic potentials that occur with time-dependent rates. The resulting process is characteriz...
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AIMS Press
2013-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.285 |
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| author | Virginia Giorno Serena Spina |
| author_facet | Virginia Giorno Serena Spina |
| author_sort | Virginia Giorno |
| collection | DOAJ |
| description | An Ornstein-Uhlenbeck diffusion process is considered as a model for the membrane potential activity of a single neuron. We assume that the neuron is subject to a sequence of inhibitory and excitatory post-synaptic potentials that occur with time-dependent rates. The resulting process is characterized by time-dependent drift. For this model, we construct the return process describing the membrane potential.It is a non homogeneous Ornstein-Uhlenbeck process with jumps on which the effect of random refractoriness is introduced. An asymptotic analysis of the process modeling the number of firings and the distribution of interspike intervals is performed under the assumption of exponential distribution for the firing time.Some numerical evaluations are performed to provide quantitative information on the role of the parameters. |
| format | Article |
| id | doaj-art-f03e21b52609489799a2255fcac992a6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f03e21b52609489799a2255fcac992a62025-01-24T02:28:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-09-0111228530210.3934/mbe.2014.11.285On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal modelVirginia Giorno0Serena Spina1Dipartimento di Studi e Ricerche Aziendali (Management &Information Technology), Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA)Dipartimento di Matematica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA)An Ornstein-Uhlenbeck diffusion process is considered as a model for the membrane potential activity of a single neuron. We assume that the neuron is subject to a sequence of inhibitory and excitatory post-synaptic potentials that occur with time-dependent rates. The resulting process is characterized by time-dependent drift. For this model, we construct the return process describing the membrane potential.It is a non homogeneous Ornstein-Uhlenbeck process with jumps on which the effect of random refractoriness is introduced. An asymptotic analysis of the process modeling the number of firings and the distribution of interspike intervals is performed under the assumption of exponential distribution for the firing time.Some numerical evaluations are performed to provide quantitative information on the role of the parameters.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.285jump diffusion processconstant refractorinessexponential refractoriness.ornstein-uhlenbeck process |
| spellingShingle | Virginia Giorno Serena Spina On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model Mathematical Biosciences and Engineering jump diffusion process constant refractoriness exponential refractoriness. ornstein-uhlenbeck process |
| title | On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model |
| title_full | On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model |
| title_fullStr | On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model |
| title_full_unstemmed | On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model |
| title_short | On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model |
| title_sort | on the return process with refractoriness for a non homogeneous ornstein uhlenbeck neuronal model |
| topic | jump diffusion process constant refractoriness exponential refractoriness. ornstein-uhlenbeck process |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.285 |
| work_keys_str_mv | AT virginiagiorno onthereturnprocesswithrefractorinessforanonhomogeneousornsteinuhlenbeckneuronalmodel AT serenaspina onthereturnprocesswithrefractorinessforanonhomogeneousornsteinuhlenbeckneuronalmodel |