We report new organized structures in bi-parameter space for a nonlinear discrete predator-prey model with hunting cooperation. The intrinsic hunting cooperation among predator populations alters the dynamical behaviors of the model significantly. Especially, the stable periodic organized structures, viz. the Arnold tongues and shrimp-shaped structures in quasi-periodic and chaotic regimes exist near the boundary of Neimark-Sacker bifurcation for moderate values of the hunting cooperation parameter. Interestingly, these regular structures lead to different period-adding sequences. The transition to chaos via period-bubbling cascade near the inner boundaries of the shrimp-shaped structures is obtained. Shrimp structures maintain the universality of period 3-times self-similarity. Also, the coexistence of multiple periodic cycles and chaotic attractors with fractal basin boundaries are found owing to the hunting cooperation among the predators.

我们报告了具有狩猎合作的非线性离散捕食者-猎物模型在双参数空间中的新组织结构。捕食者种群之间的内在狩猎合作极大地改变了模型的动力学行为。特别是稳定的周期性组织结构。在Neimark-Sacker分叉的边界附近存在准周期性和混沌状态下的Arnold舌和虾形结构，以获取适度的狩猎合作参数。有趣的是，这些规则结构导致不同的周期添加序列。在虾形结构的内部边界附近，通过周期性冒泡的级联转变为混沌。虾结构保持周期3倍自相似性的普遍性。也，