Weakly nonlinear analysis of a system with nonlocal diffusion

Abstract

We study, through a weakly nonlinear analysis, the pattern formation for a system of partial differential equations of the Shigesada-Kawasaki-Teramoto type with nonlocal diffusion in the one-space dimensional case with periodic boundary conditions. We obtain the pattern of the solutions for values of the bifurcation parameter in the proximity of the onset of instabilities. Finally, we compare the results of the nonlocal model with those of the usual local diffusion model.