I pulled the equations from Parameter estimation in hindmarsh-rose neurons (Steur, 2006), equation 4.1. The Hindmarsh-Rose, Hodgkin–Huxley, and other mathemati

I pulled the equations from Parameter estimation in hindmarsh-rose neurons (Steur, 2006), equation 4.1. The Hindmarsh-Rose, Hodgkin–Huxley, and other mathematical models are phenomenological models. They are meant to reproduce the observable characteristics, like the peak potential, bursting behaviour, refractory period, things like that. They can reproduce the traces of biological neurons with good accuracy (like the link in the GP), and the papers describing the model mention ion channels and whatnot, but they're very abstract. They're not made to reproduce the biology.