The Study In Behavior Of Several Types Of Biological Dynamical System

The need for describing natural system impels the evolution of mathematical biologicalmodels.The discussions of continuous biological dynamical systems were main researchdirection in the past decades. In this thesis, we considered models of several populationdynamical systems and discussed their dynamical behaviors.This paper consists of three parts.Firstly, we considered the dynamic behaviors of a mathematical chemostat modelwith variable yield and nutrient recycling and periodically impulsive perturbation on substrate.Using Floquet theory and small amplitude perturbation method, we established the conditionwhich the boundary periodic solution was globally asymptotically stable. Moreover thepermanence of the system was discussed in detail.Secondly, we study a modified Leslie-Gower and Holling-type II predator-prey model withdistributed time delay and harvest. It shows that this model exhibits two bifurcation phenomenaat the intersampling instants. One is saddle-node bifurcation and the other is singular inducedbifurcation.Thirdy, we investigate a stochastic ratio-dependent predator-pest model with stage-structure.Our model take white noise into account. We will show that the model has a positive uniquesolution in the global. We obtain the condition, guaranteeing the persistence of the model.