ON THE DYNAMICS OF THE HODGKIN-HUXLEY NEURAL MODEL: A STABLE ANALYSIS USING HURWITZ POLYNOMIALS

Abstract

In this paper, a study of the dynamics of the Hodgkin-Huxley neural model is conducted. This stability study is performed using the stability criteria for obtaining Hurwitz polynomials that provide necessary and/or sufficient conditions to analyze the dynamics of the model by studying the location of the roots of the characteristic polynomial associated with it. The main objective of the article is to analyze the stability of the Hodgkin-Huxley neural model using an analytical technique to establish Hurwitz type polynomials. This article describes and presents an analytical method to analyze the stability of the Hodgkin-Huxley neural model based on obtaining Hurwitz polynomials through stability criteria. This technique allows establishing the asymptotic stability of the neural model through the localization of the Eigen values of the matrix associated with the model. The results of this research allow establishing asymptotic stability conditions of the Hodgkin-Huxley neural model that allow analyzing the dynamics of the model. Through this article, it is possible to analyze the dynamics of the Hodgkin-Huxley neural model and allows drawing inferences regarding the initiation and transmission of action potentials in neurons and cardiac cells using the Hurwitz polynomial technique.