In this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover, the Allee effect in the predator growth is added into account from both biological and mathematical points of view. We explore the influence of the Allee and fear effect on the existence of all positive equilibria. Furthermore, the local stability properties and possible bifurcation behaviors of the proposed system about positive equilibria are discussed with the help of trace and determinant values of the Jacobian matrix. With the help of Sotomayor’s theorem, the conditions for existence of saddle-node bifurcation are derived. Also, we show that the proposed system admits limit cycle dynamics, and its stability is discussed with the value of first Lyapunov coefficient. Moreover, the numerical simulations including phase portrait, one- and two-parameter bifurcation diagrams are performed to validate our important findings.

在本文中，我们讨论了 Leslie-Gower 比率依赖的捕食者-猎物模型在猎物种群中包含恐惧的动态。此外，从生物学和数学的角度考虑了捕食者生长中的 Allee 效应。我们探讨了 Allee 和恐惧效应对所有正均衡存在的影响。此外，在雅可比矩阵的迹值和行列式值的帮助下，讨论了所提出的系统关于正平衡的局部稳定性特性和可能的​​分叉行为。借助索托马约尔定理，推导出鞍结分岔存在的条件。此外，我们表明所提出的系统承认极限循环动力学，并用第一李雅普诺夫系数的值讨论了其稳定性。而且，