A discrete spatially varying population model (original) (raw)

We will consider a discrete population model on a one-dimensional spatial grid where the local dynamics are given by the standard logistic population model. We will show that the usual approach for partial differential equations will not work in the difference equation approach. Therefore, for the PdE (partial difference equation) model we find that we cannot have migration and reproduction occurring simultaneously. We introduce a new model for the biological problem. We will give a limited number of analytic results and several numerical examples for both Neumann and Dirichlet-like boundary conditions.