The Lotka-Volterra models with nonlocal cross-diffusivity terms

Abstract

We consider the Lotka-Volterra systems in their three classic forms: competition, prey-predator, and cooperation. These systems include nonlocal cross-diffusivity terms, meaning that the diffusion velocity rate of one species depends on the total population of the other species. The inclusion of these nonlocal diffusivity terms causes a significant change in the structure of coexistence states compared to the classical Lotka-Volterra systems. To obtain these results, we employ mainly the fixed point index in cones.