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bioRxiv · 10.1101/2022.01.15.476459

Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris-Lecar model to a delay differential equation

Paraskevov, A. V.
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Abstract

Starting with the classical biophysical Morris-Lecar model of neuronal excitability, we introduce a functional analog of the Hutchinson equation initially obtained for population dynamics with delayed negative feedback. It is shown that the resulting equation with a fixed time delay qualitatively reproduces the dynamics of the original model upon direct current stimulation, preserving both the initial type of neuronal excitability and biophysically realistic spike shape within a wide range of the delay values. If the delay becomes very small (2 ms or less), the simplified delay-based model exhibits a distinct transition from the 1st to the 2nd excitability type.

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Paraskevov, A. V.. 2022-01-18. Analog of the Hutchinson equation in biophysical neurodynamics: from the Morris-Lecar model to a delay differential equation. https://doi.org/10.1101/2022.01.15.476459

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