From 6c9ec4f093ecfa48fe3a4a3fa99de16c5676d7dc Mon Sep 17 00:00:00 2001
From: bnewbold <bnewbold@robocracy.org>
Date: Mon, 16 Jan 2017 16:24:09 -0800
Subject: update remaining models

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+
+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.
+
+## Mathematical properties
+
+The Hodgkin–Huxley model can be thought of as a differential equation with four
+state variables, v(t), m(t), n(t), and h(t), that change with respect to time
+t. The system is difficult to study because it is a nonlinear system and cannot
+be solved analytically. However, there are many numeric methods available to
+analyze the system. Certain properties and general behaviors, such as limit
+cycles, can be proven to exist.
+
+## Alternative Models
+
+The Hodgkin–Huxley model is regarded as one of the great achievements of 20th-century biophysics. Nevertheless, modern Hodgkin–Huxley-type models have been extended in several important ways:
+
+* Additional ion channel populations have been incorporated based on experimental data.
+
+* The Hodgkin–Huxley model has been modified to incorporate transition state
+  theory and produce thermodynamic Hodgkin–Huxley models.
+
+* Models often incorporate highly complex geometries of dendrites and axons,
+  often based on microscopy data.
+
+* Stochastic models of ion-channel behavior, leading to stochastic hybrid
+  systems
+
+Several simplified neuronal models have also been developed (such as the
+FitzHugh–Nagumo model), facilitating efficient large-scale simulation of groups
+of neurons, as well as mathematical insight into dynamics of action potential
+generation.
+
+
+## References
+
+The body of this page is from Wikipedia (see below).
+
+#### Papers
+
+"The dual effect of membrane potential on sodium conductance in the giant axon
+of Loligo". *The Journal of Physiology*. **116** (4): 497–506. April 1952.
+doi:10.1113/jphysiol.1952.sp004719.
+
+"Currents carried by sodium and potassium ions through the membrane of the
+giant axon of Loligo". *The Journal of Physiology*. **116** (4): 449–72. April 1952.
+doi:10.1113/jphysiol.1952.sp004717.
+
+"The components of membrane conductance in the giant axon of Loligo". *The
+Journal of Physiology*. **116** (4): 473–96. April 1952.
+doi:10.1113/jphysiol.1952.sp004718.
+
+"The dual effect of membrane potential on sodium conductance in the giant axon
+of Loligo". *The Journal of Physiology*. **116** (4): 497–506. April 1952.
+doi:10.1113/jphysiol.1952.sp004719.
+
+"A quantitative description of membrane current and its application to
+conduction and excitation in nerve". *The Journal of Physiology*. **117** (4):
+500–44. August 1952. doi:10.1113/jphysiol.1952.sp004764.
+
+#### Interactive Models on the Web
+
+* ModelDB: [Squid axon (Hodgkin, Huxley 1952)](https://senselab.med.yale.edu/ModelDB/ShowModel.cshtml?model=5426)
+* Wolfram Demonstrations:
+  [Interactive Hodgkin-Huxley](http://demonstrations.wolfram.com/HodgkinHuxleyActionPotentialModel/)
+  by Shimon Marom and
+  [Neural Impulses: The Action Potential in Action](http://www.demonstrations.wolfram.com/NeuralImpulsesTheActionPotentialInAction/)
+  by Garrett Neske
+* [Hodgkin-Huxley Simulation with Javascript](http://myselph.de/hodgkinHuxley.html)
+  by Hubert Eichner, which creates static plots in the browser.
+* BioModels database: [](http://www.ebi.ac.uk/biomodels-main/BIOMD0000000020)
+
+#### Other Links
+
+* Wikipedia: [Hodgkin–Huxley model](https://en.wikipedia.org/wiki/Hodgkin%E2%80%93Huxley_model)
+* [Summary of the Hodgkin-Huxley model](http://ecee.colorado.edu/~ecen4831/HHsumWWW/HHsum.html)
+* [Hodgkin-Huxley model in R](http://www.magesblog.com/2012/06/hodgkin-huxley-model-in-r.html)
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