Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons
With the aim to describe the interaction between a couple of neurons a stochastic model is proposed and formalized. In such a model, maintaining statements of the Leaky Integrate-and-Fire framework, we include a random component in the synaptic current, whose role is to modify the equilibrium point...
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| Format: | Article |
| Language: | English |
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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.2014.11.189 |
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| author | Aniello Buonocore Luigia Caputo Enrica Pirozzi Maria Francesca Carfora |
| author_facet | Aniello Buonocore Luigia Caputo Enrica Pirozzi Maria Francesca Carfora |
| author_sort | Aniello Buonocore |
| collection | DOAJ |
| description | With the aim to describe the interaction between a couple of neurons a stochastic model is proposed and formalized. In such a model, maintaining statements of the Leaky Integrate-and-Fire framework, we include a random component in the synaptic current, whose role is to modify the equilibrium point of the membrane potential of one of the two neurons and when a spike of the other one occurs it is turned on. The initial and after spike reset positions do not allow to identify the inter-spike intervals with the corresponding first passage times. However, we are able to apply some well-known results for the first passage time problem for the Ornstein-Uhlenbeck process in order to obtain (i) an approximation of the probability density function of the inter-spike intervals in one-way-type interaction and (ii) an approximation of the tail of the probability density function of the inter-spike intervals in the mutual interaction. Such an approximation is admissible for small instantaneous firing rates of both neurons. |
| format | Article |
| id | doaj-art-2634fe67507849d7b5cc650e8261f3fa |
| 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-2634fe67507849d7b5cc650e8261f3fa2025-01-24T02:28:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-09-0111218920110.3934/mbe.2014.11.189Gauss-diffusion processes for modeling the dynamics of a couple of interacting neuronsAniello Buonocore0Luigia Caputo1Enrica Pirozzi2Maria Francesca Carfora3Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 NapoliDipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 NapoliDipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 NapoliIstituto per le Appplicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, Via Pietro Castellino, NapoliWith the aim to describe the interaction between a couple of neurons a stochastic model is proposed and formalized. In such a model, maintaining statements of the Leaky Integrate-and-Fire framework, we include a random component in the synaptic current, whose role is to modify the equilibrium point of the membrane potential of one of the two neurons and when a spike of the other one occurs it is turned on. The initial and after spike reset positions do not allow to identify the inter-spike intervals with the corresponding first passage times. However, we are able to apply some well-known results for the first passage time problem for the Ornstein-Uhlenbeck process in order to obtain (i) an approximation of the probability density function of the inter-spike intervals in one-way-type interaction and (ii) an approximation of the tail of the probability density function of the inter-spike intervals in the mutual interaction. Such an approximation is admissible for small instantaneous firing rates of both neurons.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.189leaky integrate-and-fire modelstochastic connectionsynaptic currentasymptotic behavior.first passage time |
| spellingShingle | Aniello Buonocore Luigia Caputo Enrica Pirozzi Maria Francesca Carfora Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons Mathematical Biosciences and Engineering leaky integrate-and-fire model stochastic connection synaptic current asymptotic behavior. first passage time |
| title | Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons |
| title_full | Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons |
| title_fullStr | Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons |
| title_full_unstemmed | Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons |
| title_short | Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons |
| title_sort | gauss diffusion processes for modeling the dynamics of a couple of interacting neurons |
| topic | leaky integrate-and-fire model stochastic connection synaptic current asymptotic behavior. first passage time |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.189 |
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