Global stability of traveling wave fronts for a reaction-diffusion system with a quiescent stage on a one-dimensional spatial lattice.

This paper is concerned with the stability of traveling wave fronts for a coupled system of non-local delayed lattice differential equations with a quiescent stage. It shows that under certain conditions all non-critical traveling wave fronts are globally exponentially stable, and critical ftraveling wave fronts are globally algebraically stable by applying the weighted energy method and the semi-discrete Fourier transform. [ABSTRACT FROM AUTHOR]