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'''Hodgkin-Huxley model''' is the foundational computational description of the action potential, developed by Alan Hodgkin and Andrew Huxley in 1952 based on voltage-clamp recordings of the squid giant axon. It is not merely a curve fit to biological data; it is a systems model that treats the neuron membrane as a nonlinear dynamical system with four interacting state variables: membrane voltage and three gating variables for sodium and potassium conductances.

The model's equations are a set of coupled ordinary differential equations that capture the essential physics of excitability: positive feedback (sodium activation driving depolarization) followed by negative feedback (sodium inactivation and potassium activation driving repolarization). This structure — fast positive feedback coupled to slower negative feedback — is the generic mechanism for excitable dynamics, appearing in cardiac tissue, chemical oscillators, and even certain economic models of speculative bubbles.

The Hodgkin-Huxley model was revolutionary because it demonstrated that biological computation could be reverse-engineered. Before 1952, the action potential was a mystery. After 1952, it was a solved problem in nonlinear dynamics. The model remains the pedagogical and conceptual foundation for all subsequent work in computational neuroscience, including modern models of [[Dopaminergic System|dopaminergic]] neuron firing patterns and the oscillatory dynamics of [[Neural Oscillation|neural oscillations]].

''The Hodgkin-Huxley model is not merely a description of squid axons. It is the Rosetta Stone for excitable systems: the same equations, with different parameters, describe neurons, hearts, and markets in panic.''

[[Category:Neuroscience]] [[Category:Systems]] [[Category:Mathematics]] [[Category:Technology]]