This paper investigates the rich dynamics in a tritrophic food chain mathematical model, consisting of three species: prey, intermediate predators, and top predators. It is assumed that alternative food are supplied to intermediate predators in addition to feeding on prey. We consider a general Holling type response function and analyze the model. The existence and stability of six possible equilibrium points are established. These equilibrium points describe the various dynamics that could take place in the food chain. Hopf bifurcation, limit cycle, doubling periods, chaotic attractors, boundary crisis are observed in the numerical computations. Our results reveal the rich and complex dynamics of the interactions in the food chain.

中文翻译：

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具有一般功能响应的三营养食物链模型中的复杂动力学

本文研究了三营养食物链数学模型中的丰富动力学，该模型由三种物种组成：猎物，中间食肉动物和顶级食肉动物。假定除了以猎物为食以外，还向中间捕食者提供替代性食物。我们考虑一般的Holling型响应函数并分析模型。建立了六个可能的平衡点的存在性和稳定性。这些平衡点描述了食物链中可能发生的各种动态。在数值计算中观察到霍普夫分叉，极限环，倍增周期，混沌吸引子，边界危机。我们的结果揭示了食物链中相互作用的丰富而复杂的动力学。