| In population ecology the interaction among species and the relationship between environment and species can be revealed from the viewpoint of dynamics. Predator-prey dynamical system which is a hot topic in filed of mathematical biology and population ecology can describe,predict and control the development of species.Traditional predator-prey model mainly focus on predator-prey relationship and intraspecific mutual interference of predators. However, if there exist more than one predator specie in the ecological system, the interspecies interference among them plays an important role during the evolution of ecological system, which can not be ignored when we establish the dynamical model.Based on the document [35], three species of predator-prey model involving non-monotonic functional response, nonlinear density dependence and interspecies mutual interference is created. In the first chapter, we introduce the background and research significance of problems which will be investigated as well as main work of this paper. At same time the review of existing research results, together with some basic theory concerning the qualitative theory and stability theory of ordinary differential equation are given. In the second chapter, local and global stability of equilibrium is analyzed by using qualitative analysis and stability theory of ordinary differential equation. In the third chapter the sufficient conditions of permanence are obtained and the Hopf bifurcation of system is studied when the parameters of model change. Moreover theoretical analyses are verified by numerical simulation. The finding shows that the interaction among three species may cause one of predator species becomes extinct, the other two species coexist in the form of positive equilibrium state or periodic oscillation; or both of them become extinct; or all three species tend to permanent state. |
PDF Full Text Request