Global stability of traveling waves for non-monotone lattice differential equations with time-delay

This paper is concerned with the global stability of traveling waves for non-monotone infinite-dimensional lattice differential equations with time delay. By establishing the boundedness estimate of the solution of the perturbation equation, we obtain that, for any initial perturbations around the traveling wave, the noncritical traveling waves are globally stable with the exponential convergence rate t(-1/alpha e-mu t) (mu > 0 and 0 < alpha <= 2), and the critical traveling waves are globally stable with the algebraic convergence rate t(-1/)alpha in a weighted Sobolev space.