A predator–prey system in discrete-time for which the predators engage in cooperative hunting and the prey population is subject to scramble intra-specific competition is developed and analyzed. We prove that the number of positive equilibrium points depends not only on the predator’s basic reproduction number but also on the intensity of predator cooperation. The model exhibits a discrete Hopf bifurcation when the unique positive equilibrium point loses its stability. Two-parameter bifurcation diagrams using MATLAB conclude that hunting cooperation can increase the likelihood of predator persistence but may destabilize the predator–prey interaction and drive the predator to extinction.

开发和分析了一个离散时间的捕食者-猎物系统，其中捕食者参与合作狩猎，猎物种群受到种内竞争。我们证明了正平衡点的数量不仅取决于捕食者的基本繁殖数，还取决于捕食者合作的强度。当唯一的正平衡点失去稳定性时，模型表现出离散的 Hopf 分岔。使用 MATLAB 的双参数分叉图得出结论，狩猎合作可以增加捕食者持续存在的可能性，但可能会破坏捕食者-猎物相互作用的稳定性并导致捕食者灭绝。