In the present paper, we report the effect of nanoparticles in a three-species aquatic food chain model. It is assumed that due to the unavoidable interactions with nanoparticles, the growth rate of basal prey reduces. Fascinating dynamical scenarios in the model are explored in different bi-parametric spaces. We show that the model exhibits coexisting attractors of different kinds (periodic–periodic/periodic–chaotic) in some regions of the bi-parametric space. We also discover well-organized shrimp-shaped periodic structures in the chaotic regime, indicating the coexistence of order (regular pattern) and chaos. Further, a period-bubbling transition to chaos is found near the inner boundaries of the shrimp-shaped structure. It is also observed that managing the depletion rate of the nanoparticles can be used as a control strategy to prevent population extinction in an aquatic food chain system.

在本论文中，我们报告了纳米粒子在三种水生食物链模型中的作用。假设由于与纳米粒子不可避免的相互作用，基础价格的增长率降低。在不同的双参数空间中探索了模型中迷人的动态场景。我们表明，该模型在双参数空间的某些区域中表现出不同类型（周期性 - 周期性 / 周期性 - 混沌）的共存吸引子。我们还在混沌状态中发现了组织良好的虾形周期结构，表明秩序（规则模式）和混沌并存。此外，在虾形结构的内部边界附近发现了一个周期冒泡过渡到混沌。