Existence And Stability For Several Classes Of Biomathematics Model

In the paper, we mainly study a few kinds of predator-prey system with Hassell-Varelyfunctional response. Then combing with feedback control, diffusion, and periodic harvest, weestablish two kinds of biological models. At last, by using continuation theorem of degree theory,some sufficient conditions for the existence of periodic solutions are obtained.This paper consists of five chapters, and the concrete structure is as follows:In chapter1, we introduce the model we will study, main work of this paper, preparingknowledge and some notions.At present, there are few literatures discussing the spices growth fit Gompertz model,however, in nature, the Gompertz model fit well for many spices. Therefore, in chapter2, apredator-prey system for Gompertz model with feedback control is studied. By using the Mawhincontinuation theorem, the sufficient conditions for the existence of periodic solutions are obtained.And then by constructing a suitable Lyapunov function, the global attractivity of positive periodicsolution are presented.In chapter3, we study a discrete two predators one prey system. In this chapter, we firstly setup a differential equation system with Hassell-varely functional response, then discrete it. Byapplying continuation theorem in coincidence degree, we obtain sufficient conditions whichguarantee the existence of at least one positive periodic solution of this system.Periodic harvest is hot research in recent years, so in the chapter4, a predator-prey systemwith diffusion and impulsive effects is considered. with the continuation theorem of coincidencedegree theory and relative continuous theorem, we obtain the existence of a positive periodicsolution for such a system. Furthermore, we show that all the solutions to the system are uniformlyupper bound.Chapter5for the conclusion, the paper mainly summarizes the main content, and points outthe defects of the paper and the future research direction.