104
∂t
Cm vs
1 —2 1
1 -1
Ww
Cmys
0
О
(Φ(ws(t))e).(vs(t) + vs) - Φ(ws(t))Ei
О
О
(Φ(ws)e).vs(i) - Φ(ws)Ei
ɪ [BIω(i)
2πα∆rr Is(t)
ws(t) = (a(vs(*) + vs) - ws(t)).∕B(vs(t) +vs),
(4-9)
(4.Ю)
where vs ∈ Rλ's, vw ∈ R-7v,", and ww ∈ Rλ,,""ii and where Q ∈ lR7vRm+i)×7Mm+i)
is the quasi-active system matrix, B =
I∕Cm
^u,(m+l)x‰ Js the quasj.
active input matrix, c = 2/?а(кж)2 ’ an^ where e^w ∈ R^'Rm+1) ⅛ the coordinate
vector corresponding to Nw. The definitions of the ionic term Φ and the strong
gating variables ws follow as in §3, just adjusted to the proper number of strong
compartments.
Notice that the nonlinear term Φ has been split into two parts, one at which
to evaluate the ionic currents at the absolute strong voltage and one at the resting
strong voltage. This is because the state variables are with respect to rest, but Φ takes
absolute voltage values, implying that the ionic term is not computed with respect
to rest, unlike the other quantities in the system. This nonlinear ionic contribution
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