Turing instability in oscillator chains with non-local coupling
  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. 
R. L. Viana, F. A. dos S. Silva, and S. R. Lopes
nlin.PS nlin.AO