Positive Periodic Solution For Predator-prey System With Sparse Effect And Functional Response

In this paper, we discuss the following applied problems about two aspects by usingthe continuation theorem based on coincidence degree theory.Firstly, the existence of positive periodic solution for a periodic predator-prey systemwith sparse effect and Holling â…¢ type functional response is studied in chapter 2. A setof sufficient conditions is derived about it, which improve some known results.Secondly, by using the coincidence degree theory based on the chapter 2, theexistence of positive periodic solution for a periodic predator-prey system with sparseeffect and Beddington-DeAngelis functional response is studied in chapter 3. If s (t ) = 0in this model, which is a general form of the classical predator-prey system withBeddington-DeAngelis functional response. A sufficient condition is also derived about it,which improve some known results.