Existence,Uniqueness and Asymptotic Stability of Traveling Wavefronts in A Non-Local Delayed Diffusion Equation

In this paper, we study the existence, uniqueness, and global asymptotic stability of traveling wave fronts in a non-local reaction–diffusion model for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment. Under realistic assumptions on the birth function, we construct various pairs of super and sub solutions and utilize the comparison and squeezing technique to prove that the equation has exactly one non-decreasing traveling wavefront (up to a translation) which is monotonically increasing and globally asymptotic stable with phase shift.