On some quasilinear structured population models

Abstract

The object of my research was the mathematical analysis of a class of population models in which the effect of differences of individuals (in e.g. age, size or position in space) on their physiological development, mortality and reproduction is assumed to play an important role. Such models, which are known as structured population models, have applications in ecology, epidemiology or medicine. If the development of individuals is dependent on the present population state, we speak of quasilinear models and it is on these models that the research focuses. For a rather large class of quasilinear populations we established growth bounds. Another result is that small changes in the composition of the population at a given moment in time can result only in small changes of the composition in the future. Similarly, for many populations in a certain sense there can not occur a jump in the composition, if the time interval of observation is sufficiently small. Additionally we elaborated a steady state analysis with bifurcation methods for a cannibalistic population structured by individual body size. Finally, we investigated criteria for the stability of steady states, in terms of solutions of a characteristic equation.