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

Abstract 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 / α e − μ t for some constants μ > 0 and 0 α ≤ 2 , and the critical traveling wave fronts are globally stable in the algebraic form of t − 1 / α .

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