Distributed modelling of deterministic and stochastic population dynamics

In many problems of practical purpose, one is interested not only in the study of the total population of the overall system, but also in the distribution of the population depending upon some characteristic parameters. This necessity is patent in biological systems defined on a wide range of distributed features, but it is also in order when one tries to analyze social systems by means of population models. As a matter of fact, with this objective in mind, we deal with infinite species population models.This study discusses this question, proposes a distributed version for the logistic equation, and examines the existence of stationary solutions. The problem of the influence of environmental noise on the dynamics of the distributed population is considered, and a model is proposed. A detailed analysis is carried out around the stationary solution via a linearization technique, and the covariance equation is derived.