  A class of systems is considered, where immobile species associated to
distinct patches, the nodes of a network, interact both locally and at a
long-range, as specified by an (interaction) adjacency matrix. Non local
interactions are treated in a mean-field setting which enables the system to
reach a homogeneous consensus state, either constant or time dependent. We
provide analytical evidence that such homogeneous solution can turn unstable
under externally imposed disturbances, following a symmetry breaking mechanism
which anticipates the subsequent outbreak of the patterns. The onset of the
instability can be traced back, via a linear stability analysis, to a
dispersion relation that is shaped by the spectrum of an unconventional
reactive Laplacian. The proposed mechanism prescinds from the classical Local
Activation and Lateral Inhibition scheme, which sits at the core of the Turing
recipe for diffusion driven instabilities. Examples of systems displaying a
fixed-point or a limit cycle, in their uncoupled versions, are discussed. Taken
together, our results pave the way for alternative mechanisms of pattern
formation, opening new possibilities for modeling ecological, chemical and
physical interacting systems.
