= Solution
The common <vector> field $F$ represents an identical reference cell. The small cell-specific term $\epsilon G_i$ represents heterogeneity of cellular properties, such as differing ion-current parameters or intrinsic <oscillation> rates. It is not external random noise: the displayed model is deterministic.
The <Kronecker delta> factors restrict coupling to the first state component, the <membrane potential>. Substitution gives a coupling current in the <voltage> equation proportional to $\epsilon\sum_jd_{ij}(u_j^1-u_i^1)$, while the other state components have no direct intercellular coupling. This is the linear voltage-difference response of <gap junctions>. Gating and chemical variables can still change indirectly through their own coupled intracellular dynamics. The zero diagonal removes self-coupling, which would contribute zero anyway. Physical reciprocal gap-junction coupling is often symmetric, but \b[zero diagonal alone does not impose reciprocity]; that distinction matters in the final part.
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