The study is an attempt to explore the competitive effects on the top predators in the tri-trophic food chain model. Holling types II and IV functional responses are used to investigate the complex behavior of the tri-trophic prey–predator system. Reaction–diffusion systems have been used to represent temporal evolution and spatial interaction among the species. Consequently, local and global stabilities, and Hopf-bifurcation have been analyzed. The numerical simulation leads to spontaneous and interesting pattern formation in two dimensions, signifying diffusion interaction between mid- and top-level predators. The effect of diffusion on the chaotic dynamics of the model systems is also investigated. It is found that the chaos mechanism wave-like behavior of the chaotic attractor exists for a long time. The diffusion of this long-term behavior is controlled by using Hybrid Control Strategy.

中文翻译：

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分叉混沌控制的种内竞争食物链系统格局形成

该研究旨在探索三营养食物链模型中对顶级捕食者的竞争影响。Holling II 型和 IV 型功能反应用于研究三营养型猎物 - 捕食者系统的复杂行为。反应扩散系统已被用于表示物种之间的时间演化和空间相互作用。因此，对局部和全局稳定性以及 Hopf 分岔进行了分析。数值模拟导致二维自发和有趣的模式形成，表明中级和顶级捕食者之间的扩散相互作用。还研究了扩散对模型系统混沌动力学的影响。发现混沌吸引子的混沌机制波状行为长期存在。