paper, In the present, and we consider a class of reaction-diffusion systems based on the Lotka-Volterra differential equation model of a predator-prey interaction with the existence of memory terms. We show that every solution with initial values in and subject to homogeneous Neumann boundary conditions decays to a spatially homogeneous function of time. 2026. “On Distributed Predator-Prey System With Memories”. Discontinuity, Nonlinearity, and Complexity 11 (3): 395-403. https://doi.org/10.5890/DNC.2022.09.003.