Dynamics Analysis Of Water-plant Model With Infiltration Feedback

In this thesis,based on infiltration feedback,we establish two water-plant model-s with two different forms of infiltration feedback.Besides,we discuss the dynamical properties and biological meanings of each model.In Chapter 1,we introduce the background and the current research status of of water-biomass dynamical models.Meanwhile some basic theory are briefly stated.In Chapter 2,In this paper,we develop a water-plant model with infiltration feed-back when palnt density is greater than a certain value.Firstly through an analysis of local stability of the equilibriums,we present existence conditions of Hopf bifurcation.Then by constructing Dulac function,we show the nonexistence conditons of limit cycle.Finally,we discuss global stability of equilibriums.In Chapter 3,we establish a water-biomass model with infiltration feedback and Holling-? function response.First of all,we prove the nonnegativity and boundedness of solutions.Then,the existence and stability of the equilibrium points are discussed.Finally,by constructing Dulac function,we show the nonexistence conditons of limit cycle.Finally,we prove global stability of equilibriums.In the last chapter,the basic results of this paper are briefly reviewed.Then we introduce the biological meaning and practical value of the model.Finally,we point out shortages of this paper and problems which need to be studied further.