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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2016, Volume 19, Number 1, Pages 87–96
DOI: https://doi.org/10.15372/SJNM20160107 (Mi sjvm604) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Probability density function of leaky integrate-and-fire model with Lévy noise and its numerical approximation

P. Singha, M. K. Kadalbajoob, K. Sharmac

a School of Mathematics and Computer Applications, Thapar University, Patiala, India
b Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India
c Department of Mathematics, South Asian University, New Delhi, India
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DOI: https://doi.org/10.15372/SJNM20160107
Abstract: We investigate a numerical analysis of a leaky integrate-and-fire model with Lévy noise. We consider a neuron model in which the probability density function of a neuron in some potential at any time is modeled by a transport equation. Lévy noise is included due to jumps by excitatory and inhibitory impulses. Due to these jumps the resulting equation is a transport equation containing two integrals in the right-hand side (jumps). We design, implement, and analyze numerical methods of finite volume type. Some numerical examples are also included.
Key words: leaky integrate-and-fire model, transport equation, finite volume approximation, Lévy noise.
Received: 25.01.2015
English version:
Numerical Analysis and Applications, 2016, Volume 9, Issue 1, Pages 66–73
DOI: https://doi.org/10.1134/S1995423916010079
Bibliographic databases:
Document Type: Article
MSC: 35L04, 65M08, 92B20
Language: Russian
Citation: P. Singh, M. K. Kadalbajoo, K. Sharma, “Probability density function of leaky integrate-and-fire model with Lévy noise and its numerical approximation”, Sib. Zh. Vychisl. Mat., 19:1 (2016), 87–96; Num. Anal. Appl., 9:1 (2016), 66–73
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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