Hodgkin-Huxley model

The Hodgkin-Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical characteristics of excitable cells such as neurons and cardiac myocytes, and hence it is a continuous time model, unlike the Rulkov map for example.

Alan Lloyd Hodgkin and Andrew Fielding Huxley described the model in 1952 to explain the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon. They received the 1963 Nobel Prize in Physiology or Medicine for this work.

The studies are usually centered in the dynamic properties of the equations as the study of the phase space and the bifurcations.

There are several of improvements and extensions of the Hodgkin-Huxley model considering other variables and equations.

See also

Dynamical systems, Differential equations, Integrate-and-fire models

Material

• ModelDB

Papers

• Hodgkin, A. L.; Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117 (4): 500-544.
• Hassard, B. (1978). Bifurcation of periodic solutions of the Hodgkin-Huxley model for the squid giant axon. Journal of Theoretical Biology, 71(3), 401-420.
• Guckenheimer, J., & Oliva, R. A. (2002). Chaos in the Hodgkin–Huxley Model. SIAM Journal on Applied Dynamical Systems, 1(1), 105-114.
• Abbott, L. F., & Kepler, T. B. (1990). Model neurons: from hodgkin-huxley to hopfield. In Statistical mechanics of neural networks (pp. 5-18). Springer Berlin Heidelberg.
• Kistler, W. M., Gerstner, W., & van Hemmen, J. L. (1997). Reduction of the Hodgkin-Huxley equations to a single-variable threshold model. Neural Computation, 9(5), 1015-1045.