Stability of Traveling Waves in Noncooperative Systems With Nonlocal Dispersal of Equal Diffusivities

In this work, we first prove a stability theorem for traveling waves in a class of noncooperative reaction–diffusion systems with nonlocal dispersal of equal diffusivities. Our stability criterion is in the sense that the initial perturbation is such that a suitable weighted relative entropy function along with its Fourier transform are integrable. Then we apply our main theorem to derive the stability of traveling waves for some specific examples of noncooperative systems arising in ecology and epidemiology.