Study On Predator-prey Systems With Holling-(n+1) Type Functional Response

The study on ecological systems of species has been an important research area in biological mathematics. The ecological systems of species are controlled not only by the intrinsic attributes of species but also influenced by environmental factors. In real situations, a system is often perturbed by white noise. Whether the presence of white noise influences the properties of an ecological system or not has attracted the interest of many researchers, and a lot of research work has been done in this area.This thesis studies the properties of some prey-predator systems with Holling-(n+1) type functional response which is a generalization of Holling-II type functional response. Firstly, a class of systems is studied in the determinate case. The behavior of the system's equilibrium points is studied, the existence and uniqueness of limit cycle is studied under some conditions based on the Poincare-Bendixson's theorem and Zhang Zhifen's theorem. Secondly, another class of systems with the random white noise perturbation is studied. With the presence of random white noise perturbation, this thesis proves a theorem on the existence and uniqueness of the global positive solution of the system under some conditions, and some sufficient conditions for the boundedness of the p-th moment is also given in the thesis.