A mathematical model for population distribution II: Linear systems

The present paper constitutes a continuation of a previous relevant paper, entitled “A mathematical model for population distribution†by Elias (2023), in which the general theoretical model was described, and some initial applications were presented, namely some approximations of population distribution of a one-dimensional inertial system and a special case of one-dimensional dynamic system. Herein, by using the above model, the following issues will be addressed: a) the examination of multidimensional linear systems, both inertial and dynamic, facilitating the study of polycentric cities and systems of multiple cities (metropolitan areas) and b) the variation of the population distribution due to the geographical diversifications of the habitat of the system, as in a sloped terrain or of coastal cities. For each of the above cases, their behaviour is presented by producing and analysing the corresponding equations of motion and distribution and, whenever possible, an effort has been made to qualitatively compare the theoretical results to field data.