At the time when HH published [9] their electrical model for the neuron, the structure of the neuron, the AIS and its role in the electric operation was not yet known. HH introduced the idea explicitly that the electrically equivalent circuit of a neuron is an oscillator. They did not see any structural elements on the membrane, so logically, they assumed it was a distributed resistor and capacitor, which really has resemblance with a parallelly switched oscillator. However, they made a wrong choice of the circuit type, and their choice (probably due to inertia) was repeated in good textbooks such as ([2] Figure 3.1 or [24] Figure 1.1), and it is a commonly accepted fallacy even today [1]. This wrong choice led to the need to assume a false (rectifying) ionic current and blocks understanding, among others, why AP is initiated.
From the discussion and figure above, it is clear that the right choice is a "https://www.electronics-tutorials.ws/rc/rc-differentiator.html" differentiator where ’the input signal is applied to one side of the capacitor with the output taken across the resistor’. The currents are directly created on the membrane (condenser) and the output voltage (AP) is taken across the resistor (AIS). In other words: the neuronal membrane is a serial instead of a parallel circuit, with far-reaching consequences.
For electrical modeling, we can use the approximation that a distributed condenser (the neuronal membrane) and a discrete resistor (the AIS form an circuit, see also the discussion in section 2.5.6. It is clear that all currents (including the synaptic currents, the membrane’s rush-in current, and the artificial currents either patching them directly to the membrane or clamping them to its axons) flow into the condenser (and cause potential increases calculated using the membrane’s capacitance). Furthermore, the potential drops only due to the current flowing through the AIS. It is the exact equivalent of a passive differentiator circuit: ”the input is connected to a capacitor while the output voltage is taken from across a resistance” and not to be mismatched with a passive integrator circuit where ”the input is connected to a resistance while the output voltage is taken from across a capacitor”.