In this article, we propose and analyse a predator-prey model where apart from direct predation the prey population is affected by the fear induced from predators. The reproduction of the prey population is reduced as a cost of fear. The predator is assumed to consume the prey according to ratio-dependent functional response and is also involved in intra-specific competition due to limited resources of food. Through model analysis, it has been observed that fear factor regulates the dynamics of the system in a completely different way than in the case where functional response is only prey dependent. Also, intra-specific competition among predators reduces the effect of fear and it forms a different pattern in the system dynamics than that of the effect of fear. Furthermore, the deterministic model has been extended to a stochastic model by perturbing the natural death rates of both prey and predators. It has been observed that the stochastic system possesses a unique positive solution that is globally stable with respect to anywhere in the interior of the positive quadrant. The stochastic extinction and persistence scenario for both the species have been analysed and a detailed comparison between the deterministic and stochastic models have been done through exhaustive numerical simulation. Finally, numerical simulation has been performed to figure out the impact of fear on the population dynamics.

在本文中，我们提出并分析了捕食者-猎物模型，其中除了直接捕食外，猎物种群还受到捕食者引起的恐惧的影响。作为恐惧的代价，猎物种群的繁殖减少。假定捕食者根据依赖于比率的功能反应来消耗猎物，并且由于食物资源有限，也参与种内竞争。通过模型分析，已经观察到恐惧因素以与功能反应仅依赖于猎物的情况完全不同的方式调节系统的动态。此外，捕食者之间的种内竞争减少了恐惧的影响，它在系统动力学中形成了与恐惧影响不同的模式。此外，通过扰动猎物和捕食者的自然死亡率，确定性模型已扩展为随机模型。已经观察到随机系统具有唯一的正解，该正解相对于正象限内部的任何地方都是全局稳定的。已经分析了这两个物种的随机灭绝和持久性情景，并通过详尽的数值模拟对确定性模型和随机模型进行了详细比较。最后，进行了数值模拟以计算恐惧对人口动态的影响。已经观察到随机系统具有唯一的正解，该正解相对于正象限内部的任何地方都是全局稳定的。已经分析了这两种物种的随机灭绝和持久性情景，并通过详尽的数值模拟对确定性模型和随机模型进行了详细比较。最后，进行了数值模拟以计算恐惧对人口动态的影响。已经观察到随机系统具有唯一的正解，该正解相对于正象限内部的任何地方都是全局稳定的。已经分析了这两个物种的随机灭绝和持久性情景，并通过详尽的数值模拟对确定性模型和随机模型进行了详细比较。最后，进行了数值模拟以计算恐惧对人口动态的影响。