A multi-base harmonic balance method applied to Hodgkin-Huxley model

Aymen Balti; Valentina Lanza; Moulay Aziz-Alaoui; Aymen Balti; Valentina Lanza; Moulay Aziz-Alaoui

doi:10.3934/mbe.2018036

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 3: 807-825. doi: 10.3934/mbe.2018036

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A multi-base harmonic balance method applied to Hodgkin-Huxley model

Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France

Received: 23 November 2016 Revised: 09 October 2017 Published: 01 June 2018
MSC : Primary: 34C25; Secondary: 65L10

Our aim is to propose a new robust and manageable technique, called multi-base harmonic balance method, to detect and characterize the periodic solutions of a nonlinear dynamical system. Our case test is the Hodgkin-Huxley model, one of the most realistic neuronal models in literature. This system, depending on the value of the external stimuli current, exhibits periodic solutions, both stable and unstable.
- Periodic solutions,
- harmonic balance method,
- Hodgkin-Huxley model
Citation: Aymen Balti, Valentina Lanza, Moulay Aziz-Alaoui. A multi-base harmonic balance method applied to Hodgkin-Huxley model[J]. Mathematical Biosciences and Engineering, 2018, 15(3): 807-825. doi: 10.3934/mbe.2018036

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Abstract

Our aim is to propose a new robust and manageable technique, called multi-base harmonic balance method, to detect and characterize the periodic solutions of a nonlinear dynamical system. Our case test is the Hodgkin-Huxley model, one of the most realistic neuronal models in literature. This system, depending on the value of the external stimuli current, exhibits periodic solutions, both stable and unstable.

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