RESOLUTION AND NUMERICAL SIMULATION OF A PREY-PREDATOR MODEL WITH INDIVIDUAL MIGRATION

This study concerns the numerical resolution and simulation of the Lotka-Volterra diffusive prey-predator model. This model is a system consisting of two semi-linear parabolic partial differential equations. After performing the numerical resolution using the explicit finite difference method, whose consistency and convergence are shown, we move onto the numerical simulations, which are done under MATLAB software. We started by doing several simulations in 3 dimension (3D) to see different cases. We complete the work with a 2D simulation to compare the non-diffusive case to the diffusive cases.