Qualitative Analysis Of Some Predator-Prey Models With Sexual Favoritism

Population ecology is an important part of biomathematics, it mainly uses severalmathematical tools to study the interactions between species, and the influences on the populationdynamics from the changing environment. As the most basic and the most extensive interactionbetween species, prey relationship is being turned into one of the most rapidly developing topics inpopulation ecology.Sexual favoritism is a significant factor in the process of prey, sexual favoritism may lead to agender imbalance among species, which may affect the development of the population. Researchon the role of sexual favoritism is conducive to depict the changes in species development, andhave great significance for us to protect and use the biological resources. Now, literature on the roleof sexual favoritism is not too much, this paper will consider several types of biomathematicalmodel with sexual favoritism by existing research methods.This paper is divided into five parts: the first chapter is the introduction of this paper, itintroduces some concepts and theorems for this paper using, then a general introduction on thedevelopment of the predator model is given, finally it introduces the main work in this paper; thesecond chapter is about a three species model with Holling II functional response and sexualfavoritism, we firstly consider the persistence of predator-prey model, then discuss the existenceand stability of periodic solutions by constructing a suitable Liapunov function, and finally getalmost periodic solutions, which have more universal significance; in the third chapter, a predator-prey system with stage structure is analyzed, in the model of this chapter, predator model havestage structure, and adult predator has sexual favoritism to the prey group. We discuss the modelthe persistence of the system, then obtain the sufficient condition for a unique, globallyasymptotically stable positive periodic solution; the fourth chapter considers a ratio-dependentpredator-prey model with sexual favoritism, it discusses the persistence of the model, and then usesBrouwer fixed point theorem and Liapunov method to study the existence and stability of periodicsolution; the last chapter is the paper’s conclusion, which includes research results, meanings ofwork, and research directions in the future.