In this paper, a diffusive predator-prey model subject to the zero flux boundary conditions is considered, in which the prey population exhibits social behavior and the harvesting functional of the predator population is assumed to be considered in a quadratic form. The existence of a positive solution and its bounders is investigated. The global stability of the semi trivial constant equilibrium state is established. Concerning the non trivial equilibrium state, the local stability, Hopf bifurcation, diffusion driven instability, Turing-Hopf bifurcation are investigated. The direction and the stability of Hopf bifurcation relying on the system parameters is derived. Some numerical simulations are used to extend the analytical results and show the occurrence of the homogeneous and non homogeneous periodic solutions. Further the effect of the rivalry rate on the dynamical behavior of the studied species.

本文考虑了一个零通量边界条件下的扩散捕食-被捕食模型，在该模型中，捕食被捕食者表现出社会行为，并且假设捕食被捕食者的收获函数为二次形式。研究了一个正解及其边界的存在。建立了半琐碎的恒定平衡态的全局稳定性。关于非平凡的平衡态，研究了局部稳定性，Hopf分叉，扩散驱动的不稳定性，Turing-Hopf分叉。根据系统参数推导了Hopf分叉的方向和稳定性。一些数值模拟被用来扩展分析结果，并显示了齐次和非齐次周期解的出现。