Spatiotemporal dynamics deduced by nonlocal delay competition in a diffusive Lotka-Volterra population model

In this article, under the influence of nonlocal delay competition, we are devoted to investigating spatiotemporal dynamics of a diffusive Lotka-Volterra population model. According to the different values of some parameters, the original model may be changed into Lotka-Volterra predator-prey model, cooperative population model, or competition population model. Then, through the characteristic equation analysis, we find that nonlocal delay competition can deduce the presence of Turing-Hopf bifurcation when the original model is Lotka-Volterra cooperative population model or competition population model. However, when the original model is Lotka-Volterra predator-prey model, nonlocal delay competition cannot deduce the presence of Turing-Hopf bifurcation, but delay can deduce stability switches and the presence of Hopf bifurcation. Moreover, in the known literatures, to our knowledge, reaction-diffusion model with nonlocal delay competition has been investigated more rarely, which implies that our results in this paper are new. Finally, by presenting some numerical calculations and simulations, we obtain the rich results of stable spatially homogeneous periodic solutions, spatially steady state solutions, spatially inhomogeneous periodic solutions and stability switches deduced by delay.