Seminar at SMU Delhi

We present a series of models of population dynamics, relevant to biological populations including humans. We are concerned primarily with two questions: 1) Does clusterization occur? 2) Does the population approach a steady state, and under what conditions? We examine six models, some old and some quite recent. We begin with the spatial Galton-Watson process, and also consider variants of the FKPP (Fischer-Kolmogorov-Petrovskii-Piskunov) equation, and a pair of models involving intra-population competition from Biology. Elements such as immigration, long-distance migration, and competition are alternative mechanisms that may allow the population to reach a steady state, if possibly without depending on critical settings of the parameters.