Cooperative hunting is a widespread phenomenon in the predator population which promotes the predation and the coexistence of the prey-predator system. On the other hand, the Allee effect among prey may drive the system to instability. In this work, we consider a prey-predator model with Type-III functional response involving the hunting cooperation in predator and Allee effect in the growth rate of the prey population. Here our aim mainly is to demonstrate the impact of both the Allee effect and hunting cooperation on the system dynamics. Mathematically our analysis primarily focuses on the stability of coexisting equilibrium points and all possible bifurcations that the system may exhibit. We have observed transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and SN-TC bifurcation point respectively in the course of studying the global dynamics.

合作狩猎是一种在捕食者中普遍存在的现象，它促进了捕食者与捕食者系统的共存和共存。另一方面，猎物之间的Allee效应可能会使系统不稳定。在这项工作中，我们考虑具有III型功能反应的捕食者-捕食者模型，该模型涉及捕食者中的狩猎合作以及猎物种群增长率中的Allee效应。在这里，我们的目的主要是证明Allee效应和狩猎合作对系统动力学的影响。在数学上，我们的分析主要集中在共存平衡点的稳定性以及系统可能表现出的所有可能分叉上。我们已经观察到跨临界分叉，鞍节点分叉，霍普夫分叉，