Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Howrah, 711103, India.
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Howrah, 711103, India.
Biosystems. 2020 Nov;197:104176. doi: 10.1016/j.biosystems.2020.104176. Epub 2020 Jul 3.
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.
本文提出并分析了一个捕食者-猎物模型，其中除了直接捕食外，猎物种群还会受到来自捕食者的恐惧的影响。猎物种群的繁殖会因为恐惧而减少。捕食者被假设根据比率依赖的功能反应来消耗猎物，并且由于食物资源有限，还会参与种内竞争。通过模型分析，我们发现与仅依赖猎物的功能反应的情况相比，恐惧因素以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会降低恐惧的影响，并在系统动态中形成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，将确定性模型扩展到随机模型。我们发现随机系统具有一个独特的正解，该解在正象限内部的任何位置都是全局稳定的。分析了两种物种的随机灭绝和持续存在情景，并通过详尽的数值模拟对确定性和随机模型进行了详细比较。最后，进行了数值模拟以了解恐惧对种群动态的影响。
