Probability density function of leaky integrate-and-fire model with LГЁvy noise and its numerical approximation
P. Singh1, M.K. Kadalbajoo2, K. Sharma3
1Thapar University, Patiala, India
2Indian Institute of Technology, Kanpur, India
3South Asian University, New Delhi, India
Keywords: модель с утечками В«интегрировать-и-сработатьВ», уравнение переноса, конечно-объемная аппроксимация, шум Леви, Leaky integrate-and-fire model, transport equation, finite volume approximation, LГЁvy noise
Abstract
We investigate a numerical analysis of a leaky integrate-and-fire model with Lèvy 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. Lèvy 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.
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