Global stability of traveling wave fronts for non-local delayed lattice differential equations

This paper is concerned with the global stability of traveling wave fronts of a non-local delayed lattice differential equation. By the comparison principle together with the semi-discrete Fourier transform, we prove that, all noncritical traveling wave fronts are globally stable in the form of t−1/αe−μtt−1/αe−μt for some constants μ>0μ>0 and 0<α≤20<α≤2, and the critical traveling wave fronts are globally stable in the algebraic form of t−1/αt−1/α.