Stability Analysis Of Several Population Ecological Models

This paper mainly analyzes several population ecological models and discusses the stability of the models.It is mainly divided into three parts.The first part establishes the predator-prey model of a kind of disease spreads in prey and the prey is restricted by the population density,in which the predator has no differential predation,and does not distinguish between the prey and the disease.For this model,the conditions of the boundary equilibrium point of the model are discussed,and the local stability of the boundary equilibrium points is proved by the Routh-Hurwitz discriminant method.According to the Bendixson-Dulac discriminant method,it is proved that the limit system at the disease-free equilibrium point does not exist the closed orbits all in the positive invariant set of the system,thus obtains the conclusion of the global stability of the positive solution of the limit system,and then obtains the global asymptotic stability of the disease-free equilibrium point of the original system by the limit system theory.Finally,the existence of the positive equilibrium point is discussed.The second part is a single population model with sex structure and artificial killing under the control of infertility.Because of the rampant pest,in the process of governance people found that manage harmful organisms has better effect when artificial sterilization.In this part,on the basis of reference[1],a new model is developed,which has sex structure and artificial killing,and gives the conditions of the equilibrium point of the model.The Routh-Hurwitz criterion is used to prove the local asymptotic stability of the system at zero equilibrium point and positive equilibrium point.By establishing the proper Lyapunov function and at the same time,according to the principle of LaSalle invariant set,the sufficient conditions for global asymptotic stability of the zero equilibrium point are given,which means that the extinction of harmful organisms at this time shows that the combination of artificial killing and sterility control plays an excellent role in the treatment of pest organisms.In the third part,in order to manage harmful organisms,the sterility control and the natural enemies are introduced.We establish a kind of predator-prey model with sterility control and Holling-II-type functional response,in which the predators can only prey on the fertile pests and have Holling-II-type functional response,the boundedness of the solution is discussed,and the existence conditions and local stability of zero equilibrium point,boundary equilibrium point and positive equilibrium point are proved.