In nature, vigilance is a common anti-predator strategy prey individuals employ to protect themselves from a possible attack. It gives them sufficient time to take cover or flee. Yet this seemingly profitable strategy, which lowers the number of successful predatory attacks, has a significant impact on the prey's growth rate. Researchers attribute this to reduced foraging time. In this article, we study a three-species food chain model in which both the basal prey and middle predator show active vigilance against their respective predators. Apart from the positivity, boundedness, and local stability analysis of the equilibrium points of the model, we find the conditions for global stability and the occurrence of Hopf bifurcation around the coexisting equilibrium point. Bifurcation diagrams and their corresponding Lyapunov exponent diagrams (largest and second-largest) illustrate diverse dynamical scenarios ranging from stable coexistence to periodic to chaotic oscillations. The isospike diagrams and their associated largest Lyapunov exponent diagrams in the biparametric space of basal prey's and middle predator's vigilance reveal a broader picture of the effects of different levels of vigilance on the dynamics of the system. A great deal of attention has been paid to unwrapping the complex structural beauties like shrimp-shaped periodic structures inside the chaotic sea and multistability between several sets of attractors in the overlapping zones of periodic windows. We observe that multiple coexisting attractors possess fractal basin boundaries. We also explore the dynamics of the system in two other biparametric spaces. The density variation maps at the end show the effect of vigilance on the equilibrium density of all three species. Our results suggest that vigilance promotes regularity and coexistence, but too high levels of vigilance can cause species extinction. For better visualization of the system dynamics, we provide a few high-resolution animations of the phase portraits and the basins of attraction in the supplementary material.

在本质上，警惕是猎物个人用来保护自己免受可能攻击的常见反捕食者策略。这让他们有足够的时间躲避或逃跑。然而，这种看似有利可图的策略，降低了成功的掠夺性攻击的数量，对猎物的生长速度产生了重大影响。研究人员将此归因于觅食时间的减少。在本文中，我们研究了一个三物种食物链模型，其中基础猎物和中间捕食者都对各自的捕食者表现出积极的警惕。除了对模型的平衡点进行正性、有界性和局部稳定性分析外，我们还发现了全局稳定性和在共存平衡点周围发生 Hopf 分岔的条件。分岔图及其相应的李雅普诺夫指数图（最大和第二大）说明了从稳定共存到周期性到混沌振荡的各种动态场景。基础猎物和中间捕食者警觉的双参数空间中的等峰图及其相关的最大李雅普诺夫指数图揭示了不同警戒水平对系统动力学的影响的更广泛图景。人们非常关注解开复杂的结构美，如混沌海中的虾形周期性结构以及周期性窗口重叠区域中多组吸引子之间的多稳定性。我们观察到多个共存吸引子具有分形盆地边界。我们还在另外两个双参数空间中探索了系统的动力学。最后的密度变化图显示了警惕对所有三种物种平衡密度的影响。我们的研究结果表明，警惕可以促进规律性和共存，但过高的警惕会导致物种灭绝。为了更好地可视化系统动力学，我们在补充材料中提供了一些相像和吸引力盆地的高分辨率动画。