  Reduction of a two-component FitzHugh-Nagumo model to a single-component
model with long-range connection is considered on general networks. The reduced
model describes a single chemical species reacting on the nodes and diffusing
across the links of a multigraph with weighted long-range connections that
naturally emerge from the adiabatic elimination, which defines a new class of
networked {dynamical} systems with local and nonlocal Laplace matrices. We
study the conditions for the instability of homogeneous states in the original
and reduced models and show that Turing patterns can emerge in both models.
