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 estab-lished 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.
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