Structured population dynamics and the LPA model

In this paper we will discuss the foundations of the study of population dynamics. Included in this is the setup of the matrix models that describe the populations and properties of linear and nonlinear models. A few of the basic models, such as Leslie and Ricker, are described and looked at. Equilibria of matrix models will be discussed along with theorems that describe the stability of the equilibria. We end our discussion of general models by looking at various types of bifurcations that can occur in linear and nonlinear matrix models. The LPA model, a specific model fit for flour beetles, will then be looked at including basic properties and theorems, and finally looking at some interesting bifurcations of the model.