The Qualitative Research On Two Kinds Of Lotka-Volterra Models With Continous Capture

In this thesis of master, we distinguish the type and stability of the equilibrium points of the system by computing the eigenbalue of the linearized system corresponding to the differential system coefficient matrix and using the eigenvalues of symbols. Under the system’s coefficient satisfying some certain conditions,we prove the persistence and extinction of the system through constructing function.In the first chapter, we mainly introduce the research background and status for the classical biological system Lotka-Volterra, and the main work in this paper.Otherwise,we also give some preliminary knowledge for this thesis.In the second chapter, we investigate a class of Lotka-Volterra model, which is an autonomous, continuous acquisitive system with no density restriction: We study the stability of equilibrium point for this system. Inside x, y indicates the number of two species in the t moment, E(t) indicates the fishing effort in the t moment, a,c denotes the intrinsic rate of x, y,b,d indicates the interaction coefficient between said populations, kindicates the proportion of the two species’ capture, p1, p2indicates the price of market to the two biological relatively capture the income for capture, cindicates the relative cost price after the partial income of capture for returning to the capture. Firstly, we find out the five equilibrium points of the system, and discuss the type and stability of the equilibrium points by making use of the characteristic value of the lineared matrix A of the system.In the third chapter, we studies the system which is a nonautonomous continuous capture and the dependent of the density model: We prove the persistence and extinction of the system. Here, x(t),y(t), E(t) and the coefficients have the same meaning of the previous system. And the coefficients are continuous bounded functions for the time t. Inside a1(t),c1(t) indicate its density ratio of the bilolgical. In this chapter, we obtain some sufficient conditions of the system’s persistence survivability. At the same time, we also give a sufficient condition for the species x and y extinction of the system.