Entire Solutions in Lattice Delayed Differential Equations with Non local Interaction: Bistable Cases

This paper is concerned with entire solutions of a class of bistable delayed lattice differential equations with nonlocal interaction. Here an entire solution is meant by a solution defined for all (n, t) is an element of Z x R. Assuming that the equation has an increasing traveling wave front with nonzero wave speed and using a comparison argument, we obtain a two-dimensional manifold of entire solutions. In particular, it is shown that the traveling wave fronts are on the boundary of the manifold. Furthermore, uniqueness and stability of such entire solutions are studied.