Analysis of positive equilibrium solutions of Leslie-Gower predator-prey model with defensive ability - WANG Lijuan; YANG Jiarao; JIANG Hongling; JIN Lu; YANG Fan (Xi'an Gongcheng Daxue xuebao)
Monod-Haldane functional response function is introduced into Leslie-Gower predator-prey model under the homogeneous Dirichlet boundary condition, the influence of the defensive ability of prey on the positive equilibrium solution of the predator-prey system is studied. A priori estimate, sufficient and necessary conditions for the existence and local stability of the positive equilibrium solution are established by using the maximum principle, the super and sub-solution method, bifurcation theory and stability theory. Combined with numerical simulation, the positive equilibrium solution is quantitatively analyzed. The research shows that as long as the intrinsic growth rate of prey and predator is greater than a certain constant, the coexistence mode can be generated. At the same time, the defense ability of prey has an inhibitory effect on the predator; especially when the prey has a higher growth rate, the ability of prey to resist the predator is stronger.