  We investigate analytically and numerically the conditions for the Turing
instability to occur in a one-dimensional chain of nonlinear oscillators
coupled non-locally in such a way that the coupling strength decreases with the
spatial distance as a power-law. A range parameter makes possible to cover the
two limiting cases of local (nearest-neighbor) and a global (all-to-all)
couplings. We consider an example from a non-linear auto-catalytic
reaction-diffusion model.
