Spatiotemporal pattern formation in 2D prey-predator system with nonlocal intraspecific competition

Abstract

There is growing evidence that ecological interactions are often nonlocal. Correspondingly, increasing attention is paid to mathematical models with nonlocal terms as such models may provide a more realistic description of ecological dynamics. Here we consider a nonlocal prey-predator model where the movement of both species is described by the standard Fickian diffusion, and hence is local, but the intra-specific competition of prey is nonlocal and is described by a convolution-type term with the ‘top-hat’ (piecewise-constant) kernel. The prey growth rate also includes the strong Allee effect. The system is studied using a combination of analytical tools and extensive numerical simulations. We obtain that nonlocality makes possible the pattern formation due to the Turing instability, which is not possible in the corresponding local model. We also obtain that the nonlocality creates bistability: it depends on the initial conditions which of the two spatially heterogeneous distributions emerges. Finally, we show that the bifurcation structure of the system is less sensitive to the choice of parametrization than it is in the corresponding nonspatial case, suggesting that nonlocality may decrease the structural sensitivity of the system.