具有防御能力的 Leslie-Gower 捕食食饵模型的 平衡态正解分析.

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 stabili- ty theory. Combined with numerical simulation, the positive equilibrium solution is quantitatively ana- lyzed. 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. [ABSTRACT FROM AUTHOR]