The name is absent

Figure 2.1: Circuit diagram of an integrate-and-fire cell. The voltage υ is defined as® ≡ ι⅛ >⅛t∙
Slightly edited from my Master’s thesis (Kellems, 2007).

while v(t) ≤ ½h

C_mυ'(t) = -g_L(v(t) - E_l) + ∕_stim(<)M                (²∙1)

end

The cell has surface area A and consists of a battery of voltage E_l, a capacitance
per unit area C_m. and a resistance per unit area g_L which defines the leakage current
due to CE ions. This cell is purely passive, meaning that in the absence of input
(i.e., when ∕_stimG) = θ) the voltage v will decay back to its resting value v (in this
case V = E_l). By itself, the ODE in (2.1) does not exhibit spiking behavior, but the
while condition aims to mimic spiking by instantaneously resetting the voltage to v
if v(t) > ½h, ^at which time the cell is said to have spiked (or fired).

An experimentally-derived single-compartment model that captures spiking be-
havior was introduced in 1952 by Hodgkin and Huxley. Through experiments on the
squid giant axon, they found that the spiking dynamics could be captured through
voltage-gated ionic mechanisms. Specifically, by isolating the Na⁺ and K⁺ channels,
they discovered that the flow of ions could be modeled by gating variables that ac-

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