The name is absent

16

threshold behavior, which is important in certain neuronal functions. Hence it makes
sense to consider the linearized version of the HH model in order to address these two
concepts.

Noting that v' = 0 at rest, this implies w = w ≡ w_oo(v), and thus v is computed
by solving the nonlinear equation

0 = -9l(v - E_l) - gN_am³_och_oo(υ - E_Na) - g_κn⁴_oo(υ - E_κ), (2.7)

for v, which can be done using any standard rootfinding algorithm, such as Newton’s
Method. With v in hand we can proceed with the linearization process.

Following the lead of Koch (Koch, 1999), consider a small stimulus Z_sti_m(t) =
εZ_sti_m(t)∙ Such a stimulus will give rise to perturbed voltage and gating variables,
which are assumed to be of the form

V = V + εv + O(ε²)

m = m + εm + O(ε²)

h = h + εh + (9(ε²)

n = n + εn + <9(ε²).

Upon substitution into (2.3) we can then solve for the perturbation terms of order ε,

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