Qualitative Analysis Of A Leslie Predator-Prey System

In this paper,we consider Leslie predator-prey models with competition,stage structure and food chain.This paper consists of four parts.In chapter 1,we introduce basic content of Leslie predator-prey.In chapter 2,a competitive Leslie model is proposed.We prove that the system's solution is ultimately bounded and derive the sufficient conditions of the global stability of the positive equilibrium of the model.In chapter 3,a stage-structure predator-prey model is studied.We consider that immature and mature individuals of the prey population are divided.We obtain the sufficient conditions of the uniform persistence and the global stability of positive equilibrium.In chapter 4,a food chain model is studied.We find that the trivial equilibrium and some boundary equilibrium are always unstable.This shows that the system is persistent.By constructing lyapunov function,we prove the positive equilibrium is also global stable.