Qualitative And Stability Analysis Of Three Population Models In Ecology

In this paper, by using the qualitative and stability theories and bifurcation method of ordinary differential equations, three population models in ecology are studied .The whole paper consists of four chapters.The first chapter is the introduction, the developing of ecology and the main works of the thesis is introduced, then some fundamental theories and lemmas of ecology and stability that can be used in this paper are given.In the second chapter, a class of functional response predator-prey two species model with mutual interference and density dependence is studied. Uniqueness and global stability of positive equilibrium point, non-existence of limit cycle are obtained .Last, based on these conclusions, an exact example is given.In the third chapter, the feature of a cubic Kolmogorov system with non-constant harvest is studied. Uniqueness of limit cycle and existence of at most two limit cycles are obtained. Furthermore, the numerical example and simulative result are given, which shows that harvest of the two groups is propitious to permanence of system.In the fourth chapter, an exploited delayed three species model with stage-structure is proposed. In the first part, autonomous case of this system is studied. The sufficient conditions which guarantee the permanence and global asymptotically stable of positive equilibrium are get. At the same time, the effect of delays on the stability of the system is discussed, as delays change, a small amplitude asymptotic stable periodic solution is bifurcated. Finally, the optimal harvesting is given. In the second part, the nonautonomous diffusive system is considered. The sufficient conditions which guarantee the permanence and uniqueness of global asymptotically stable positive periodic solution of the system are obtained.