Global stability analysis of the discrete time population models

This study is related to the stability analysis of the difference-time population models. In particular, the dynamic of host-parasitoid model has been studied. Firstly, the difference-time and continuous-time models were introduced by giving the basic definitions and theorems on the subject. The effect of Allee factor and immigration parameter on stability, which has an important place in stability studies of the models, are examined. Finally, the stability of host-parasitoid model depending on the particular growth function was analyzed. Also, the effect Allee factors and the migration parameters on the stability of the model are examined; and the results which are obtained were compared with each other. The theoretical results are supported by numerical simulations.