Stability and uniqueness of traveling wavefronts in a two-dimensional lattice differential equation with delay

This paper is concerned with the uniqueness and globally exponential stability of traveling wave solutions in a lattice delayed differential equation for a single species with two age classes and a fixed maturation period living in a two-dimensional spatial unbounded environment. Under bistable assumption and realistic assumption on the birth function, we construct various pairs of super- and subsolutions and employ the squeezing technique to prove that the equation has a uniqueness traveling-wave solution. Moreover, the wave front is globally asymptotic stable with phase shift. Comparing with the previous results, we consider the symmetry of the traveling wave solutions. Our results can be expended to the case with multi-dimension lattice.