A Mathematical Model For Population Distribution

In the present paper, an attempt is made to construct a deterministic mathematical simulation for population systems, by which their temporal (equation of motion) and spatiotemporal (equation of distribution) behaviour can be deduced, as solutions of the constitutional differential equations of the system. The generic formulation of the constitutional equations gives the simulation the possibility to expand to several populations, but also to parameters of different nature (say economic), by applying proper transformations according to the inner properties of each parameter. The introduction of the topographical features of such a system can be reduced to a boundary conditions problem, applied to the constitutional differential equations. Two initial applications are analyzed herein, namely a one-dimensional inertial population system, and a one-dimensional dynamic population system, where the external force corresponds to a space of constant curvature. The theoretically predicted behaviors of the population distribution of these systems are compared qualitatively to actual field data, collected from cities around the World.