| In this paper,we first consider a two-adult predator-predator system with Holling-II functional response function and distributed delay(?)We obtain the local asymptotic stability of the feasible equilibrium point by means of linearization method and analysis of the distribution of characteristic roots on the complex plane.In addition,we obtain the global asymptotic stability of semi-trivial equilibrium and positive equilibrium by using the comparison principle and upper-lower solution method.Secondly,we consider Lotka-Volterra competitive systems with nonlocal delay(?) By means of the existence theory of traveling wave solutions of the reaction diffusion equation with nonlocal delay,we prove the existence of traveling wave solutions of two semi-trivial equilibrium points connecting the system when a specific kernel function is selected and the wave velocity c is greater than a critical value.The papaer is organized as follows:In Chapter 1,we review the research background and current situation of LotkaVolterra predator-predator system,then explain the specific content of this paper.In Chapter 2,for the predators-predator system of two adult populations with Holling-II functional response function and distributed delay,firstly,we obtain the local asymptotic stability of the feasible equilibrium point by linearization method and analyzing the distribution of characteristic roots on the complex plane;then,we obtain the global asymptotic stability of the semi-trivial equilibrium point and the positive equilibrium point by means of comparison principle and upper-lower solution method.In Chapter 3,we obtain the existence of traveling wave solutions between two semitrivial equilibrium points connecting Lotka-Volterra competitive system with nonlocal delay when a particular kernel function is selected and the wave velocity c is greater than a critical value by means of the upper-lower solution method and the monotone iteration principle. |
