This paper aims at the detailed numerical analysis of a cyclic three species predator–prey model where the prey consumes only a part of the super-predator population. Such a model exists only when the prey acts as an omnivore. Here, we have investigated the dynamical behaviour of the prey, middle predator and super-predator. All the possible equilibrium points of the model are computed and the existence and stability condition of the equilibrium states are determined. The phase portraits are generated for different sets of parameter values. The long term behaviour of the system is investigated by studying the bifurcation structure and nature of the attractors, thereby identifying the domain of chaos, as each of the control parameter is varied independently. Finally, we show that a transition from chaotic domain to escape or vice-versa of the predator in a small region of the parameter plane leads to a fractal structure.

中文翻译：

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部分消耗超级捕食者的循环三物种捕食者-猎物系统中的混沌

本文旨在对循环三物种捕食者 - 猎物模型进行详细的数值分析，其中猎物仅消耗超级捕食者种群的一部分。只有当猎物作为杂食动物时，这种模型才存在。在这里，我们研究了猎物、中间捕食者和超级捕食者的动力学行为。计算模型所有可能的平衡点，确定平衡状态的存在性和稳定性条件。相图是针对不同的参数值集生成的。通过研究分岔结构和吸引子的性质来研究系统的长期行为，从而识别混沌域，因为每个控制参数都是独立变化的。最后，