Non-linear Structured Population Models

Abstract

The previous chapters mainly treated linear structured population models. However, there are just three simple asymptotic behaviors, e.g., the population dynamics is monotonically increasing, $r_{0}>0$, decreasing, $r_{0}<0$, or constant, $r_{0}=0$. In nature, most organisms persist via complicated population dynamics established over centuries. Biologists believe that density effects as well as intra-specific and inter-specific competitions are significant phenomena that complicate the population dynamics. These phenomena appear in mathematical models for biology (including human demography) as non-linear effects. Such non-linearity is a central subject in both mathematical demography and biology. This chapter deals with the analysis of non-linear effects on individual life histories and population dynamics.