25
ε is small, then the perturbed voltage and gating variables are assumed to be
vb = vb + εvb + C,(ε2)
(2.28)
wbcf = wbcf + εwbcf + O(ε2).
(2.29)
Note here that the rest values vb and wbcf are now spatially-varying. Substituting
(2.28) into (2.17), we construct a linearized model by solving for the perturbation
terms vb, wbcf of order ε. After substitution we find
Qcf
c=l
∕=ι
I 5b _ _
- (gbs + εgbs{t)')δ(x - xbs)(yb + εvb - Ebs)
(2.30)
ε¾w6c∕(t) =
wcf,∞(υb + ε⅞) - (wbcf + εwbcf)
τcf (υb + εvb)
(2.31)
The initial conditions are now
vf,(τ,0) = w6c∕(τ,0) = 0
while boundary conditions, because they are already linear, remain the same as in
(2.19), (2.20), (2.24). The soma conditions contain nonlinear terms, but they may be
linearized in the same manner as shown here.