Qualitative Analysis Of A Class Of Predator-prey Systems With Holling ⅡType Functional Response

Population ecology is an important branch of ecology. In the process of researchon population ecology, the complexity of the relationship between species broughtgreat inconvenience, so related problems should be solved by using mathematicaltheories and methods. The study of the relationship between predators and preys hasalways been a hot issue in the field of mathematics and biology. It is valuable inapplication and has practical significance. Many scholars have focused on this area,done a lot of work, and have achieved many excellent results in theory.We mainly study a class of predator-prey systems with Holling II type functionalresponse (Moussaoui system) of Five Great Lakes ecological system. And we study thesystem with constant coefficients, periodic coefficients, or continuous boundedcoefficients respectively. And we have obtained some results.In the first part, we introduce the background. In the second part, we give thebasic knowledge, and related theory for the following research. In the third part, weintroduce the Moussaoui system. In the fourth part, we make the qualitative analysis ofthe system with constant coefficients. It includes the stability of the equilibrium points,the nonexistence of the limit cycle, and the global stability of the system and so on. Inthe fifth part, we consider the Moussaoui system with the periodic coefficients, and geta sufficient condition for the existence of periodic solutions. In the sixth part, we studyon the persistence of Moussaoui system with continuous bounded coefficients. In thelast part, we give the summary and outlook of the paper.