27
The linearized synaptic input in (2.30) has the form
-⅞ynaptic(^, ʃ; f⅛)
δ{x - Xba).
To complete the linearization process, we equate the terms of order ε and arrive at
c Fc
∂tvb = T>bvb + Kb(x)υb + 52 ΣL dbcj(x)wbcf + Ль
c=l /=1
∂twbcf(t) = φbcf(x)vb + ψbcf(x)wbcf,
where
ɪ l-' ɪ kjb
КьИ = ~^-∑ Gbc(τ)Fbc(0) - ∑9bsδ(x ~ ¾)
m c=l m s=l
1 _ Fc
dbcf(x) = -γr-Gbc(x)(υb - Ec)qcfwqbccff ɪ ɪɪ ¾
___1_
r∣b 2πabC,
sb
∑gbs(t')δ(x - xbs)(υb - Ebs)
s=l
Φbcf(β'')
wc∕,∞(^⅛)
τcf(υb) ,
Mx}=^⅛)'
It is now apparent that this is a linear system for the 6th branch, namely
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