Özel Başlangıç Koşulları Altında Lineer LIF Nöron Modelinin Analizi ve Çözüm Metodu

Year 2023, Volume: 6 Issue: 3, 1785 - 1795, 04.12.2023

Yavuz Selim İşler

https://doi.org/10.47495/okufbed.1184076

Abstract

Leaky Integrate and Fire (LIF) modeli, nöronların matematiksel olarak modellenmesi ve çalışma prensiplerinin anlaşılması için yaygın olarak kullanılmaktadır. Birçok metot ve yöntem sayesinde modelin simülasyonu ve analizi yapılsa da mühendislik çalışmalarına uygun çözümlerin azlığından söz etmek mümkündür. Birinci dereceden adi diferansiyel denklemler içeren LIF modelinin çözümüne ideal başlangıç koşulları altında kolayca ulaşılırken, karmaşık şartlar sunulduğunda sonucu bulmak zorlaşmaktadır. Bu çalışmada nöronun, birim adım akımı, darbe akımı ve rastgele seçilen akım girişleri için çözümleri yapılmıştır. Böylece literatürde yer alan metotların özel durumlar ortaya çıktığında nasıl uygulanması gerektiği gösterilmiştir.

Keywords

LIF Nöron Modeli, Pasif Membran, Diferansiyel Denklemler

Analysis of Linear LIF Neuron Model under Particular Initial Value Conditions and Solution Method

Abstract

The Leaky Integrate and Fire (LIF) model is widely used for mathematical modelling of neurons and understanding their working principles. Even though model is simulated and analyzed thanks to many methods and procedures, it is possible to mention about rarity of appropriate solutions for engineering studies. While solution of LIF model involving first order ordinary differential equations is easily obtained under ideal initial conditions, finding result is getting difficult when represented with complicated circumstances. In this study solutions for step current input, pulse current and arbitrary current input of neuron are elucidated. Therefore, it is demonstrated how to apply methods in literature when particular conditions emerged.

Keywords

LIF Neuron Model, Passive Membrane, Differential Equations

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