The name is absent

The linearized synaptic input in (2.30) has the form

-⅞ynaptic(^, ʃ; f⅛)

δ{x - X_ba).

To complete the linearization process, we equate the terms of order ε and arrive at

c F_c

∂_tv_b = T>_bv_b + K_b(x)υ_b + 52 ΣL ^d_bcj(x)w_bcf + Ль

c=l /=1

∂_tw_bcf(t) = φ_bcf(x)v_b + ψ_bcf(x)w_bcf,

where

ɪ ^l-' ɪ ^kjb

КьИ = ~^-∑ G_bc(τ)F_bc(0) - ∑9_bs^δ(^x ~ ¾)

^m c=l ^m s=l

1 _ ^Fcd_bcf(x) = -γr-G_bc(x)(υ_b - E_c)q_cfw^q_b^c_c^f_f ɪ ɪɪ ¾

___1_

^r∣^b 2πa_bC,

s_b

∑gbs(t')δ(x - x_bs)(υ_b - E_bs)
s=l

Φbcf(β'')

^wc∕,∞(^⅛)
τ_cf(υ_b) ^,

^Mx}=^⅛)'

It is now apparent that this is a linear system for the 6th branch, namely