Bistable Waves For A Single Species Model With Age Structure In 2-Dimension Lattice

In order to more accurately describe the spatial-temporal patterns of the objects of study, people have derived many lattice differential systems with nonlocal effects in population biology, spatial ecology, materials and disease spread. Because they concern the spatial nonlocal effects, they show a more complex dynamic behavior than the classic. Therefore, research on such issues is of great theoretical value and practical significance.This paper study the bistable traveling waves for a single species model with age structure and a fixed maturation period in a two-dimension lattice. This model reacts the joint effect of the diffusion dynamics, the nonlocal delayed effect and the direction of propagation. With the corresponding linear problem, we obtain the existence of bistable traveling waves. By constructing various pairs of super- and subsolutions and employing the squeezing technique to prove the uniqueness with phase shift and globally exponential stability of bistable traveling waves. Compared with previous results, this paper considers the symmetry of the bistable traveling waves with arbitraryθ. These results can be expended to the case with multi-dimension lattice.