ASYMPTOTIC BEHAVIOR OF A DELAYED NONLOCAL DISPERSAL LOTKA-VOLTERRA

This paper investigates the asymptotic behavior of a nonlo cal dispersal Lotka-Volterra competitive system with time delay across the entire RN. We establish L infinity-decay estimates of solutions of linear systems converging to equilibria utilizing the Fourier transform method applied to the fundamental solution and the Fourier splitting technique. For the nonlinear time-delayed nonlocal dispersal Lotka-Volterra competitive system, we leverage the results from linear systems and obtain the long-time behavior of solutions of the nonlinear system manifesting as the form of time-exponential. More precisely, we further deduce L infinity-decay estimates of solutions of the original nonlinear system through the properties of convolution and Ho<spacing diaeresis>lder inequality. Additionally, numerical simulations are presented to bolster the principal theoretical results and illustrate that the time delay impedes species growth.