A simple spatial model of population dynamics

A mathematical model is presented that describes the dynamics of a spatially distributed population, incorporating the effects of external migration. The evolution of the population density is governed by a simple integro-differential equation. In the spatially homogeneous case, the model isreduced to the classical logistic equation with an additional constant term and its behavior is fully characterized. In the inhomogeneous case, the dynamics is examined through numerical simulations and typical long-term behavior is illustrated.