Analysis of the complicated dynamics of some harvesting models

In this paper we will study in a qualitative way discrete single species population models including harvesting. The class of models under consideration is quite general. In fact, we will study models with fixed parameter values. However, the obtained results do have implications for the models if one varies the parameters slightly. The models with so-called "Allee-effect", i.e. the population will die out whenever the size of the population is below some threshold, are included in the class of models we studied.