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The Hodgkin–Huxley Equations

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Mathematical Foundations of Neuroscience

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 35))

Abstract

All living cells have an electrical voltage, or potential difference, between their inside and outside. Since the cell’s membrane is what separates the inside from the outside, this potential difference is referred to as the membrane potential. In mathematical terms, the membrane potential V M is defined as

$${V }_{\mathrm{M}} = {V }_{\mathrm{in}} - {V }_{\mathrm{out}},$$

where V in is the potential on the inside of the cell and V out is the potential on the outside. This will change during an action potential, for example.

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Correspondence to G. Bard Ermentrout .

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Ermentrout, G.B., Terman, D.H. (2010). The Hodgkin–Huxley Equations. In: Mathematical Foundations of Neuroscience. Interdisciplinary Applied Mathematics, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87708-2_1

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