Output Stream of Leaky Integrate-and-Fire Neuron Without Diffusion Approximation

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• 作者：Alexander K. Vidybida
• 关键词：LIF neuron ; Poisson stochastic process ; Probability density function ; Output intensity
• 刊名：Journal of Statistical Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：166
• 期：2
• 页码：267-281
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics;
• 出版者：Springer US
• ISSN：1572-9613
• 卷排序：166

文摘

Probability density function (pdf) of output interspike intervals (ISI) as well as mean ISI is found in exact form for leaky integrate-and-fire (LIF) neuron stimulated with Poisson stream. The diffusion approximation is not used. The whole range of possible ISI values is represented as infinite union of disjoint intervals: \(]0;\infty [ = ]0;T_2] + \sum _{m=0}^\infty ]T_2+m\,T_3;T_2+(m+1)T_3]\), where \(T_2\) and \(T_3\) are defined by the LIF’s physical parameters. Exact expression for the obtained pdf is different on different intervals and is given as finite sum of multiple integrals. For the first three intervals the integrals are taken which brings about exact expressions with polylogarithm functions. The found distribution can be bimodal for some values of parameters. Conditions, which ensure bimodality are briefly analyzed.