In this paper, we study the dynamics of a delay differential model of predator-prey system involving teams of two-prey and one-predator, with Monod-Haldane and Holling type II functional responses, and a cooperation between the two-teams of preys against predation. We assume that the preys grow logistically and the rate of change of the predator relies on the growth, death and intra-species competition for the predators. Two discrete time-delays are incorporated to justify the reaction time of predator with each prey. The permanence of such system is proved. Local and global stabilities of interior steady states are discussed. Hopf bifurcation analysis in terms of time-delay parameters is investigated, and threshold parameters ${\tau }_1^{*}$ and ${\tau }_2^{*}$ are obtained. Sensitivity analysis that measures the impact of small changes in the model parameters into the model predictions is also investigated. Some numerical simulations are provided to show the effectiveness of the theoretical results.

在本文中，我们研究了具有两个捕食者和一个捕食者的团队，具有Monod-Haldane和Holling II型功能性反应，以及两个猎物团队之间的协作的捕食者—猎物系统的时滞差分模型的动力学。反对掠夺。我们假设捕食者呈逻辑增长，捕食者的变化率取决于捕食者的生长，死亡和种内竞争。结合了两个离散的延时来证明捕食者与每个猎物的反应时间是合理的。证明了这种系统的持久性。讨论了内部稳态的局部和全局稳定性。研究了基于时延参数的Hopf分叉分析和阈值参数${\tau }_{\mathrm{1个}}^{*}$ 和 ${\tau }_2^{*}$获得。还研究了测量模型参数微小变化对模型预测的影响的灵敏度分析。提供了一些数值模拟，以显示理论结果的有效性。