By using qualitative analysis theory of differential equation and the Pontrjagin maximum value principle, a kind of predator-prey model with HollingII functional response is investigated. This model has density restriction and has harvesting. We obtained the conditions of the existence of the boundary equilibriums and the unique positive equilibrium, and we also obtained the conditions of the global asymptotic stability of these equilibriums. We analyzed the corresponding biological significance, and gave the optimal harvesting strategy. Then we carried on the simulation to the system under a ...
