Dynamics of a predator-prey system with fear and group defense
Dynamics of a predator-prey system with fear and group defense
复制标题
DOI：
10.1016/j.jmaa.2019.123471
复制
发表时间：
2020
影响因子：
1.3
通讯作者：
S. K. Sasmal;Y. Takeuchi
中科院分区：
文献类型：
--
作者：
S. K. Sasmal;Y. Takeuchi
研究了一类捕食者-食饵相互作用模型的动力学行为，该模型包含：（1）食饵在捕食者存在时，以恐惧效应的形式降低食饵的生长速率;（2）食饵对捕食的群体防御，利用Monod-Halfmann型功能反应.此外，我们将这两个因素相互关联，通过捕食者趋性的敏感性，作为觅食和防御的总时间或能量是恒定的猎物。如果猎物投入更多的时间或精力用于群体防御，那么繁殖可能会由于这种投资而减少。我们提供了详细的数学结果，包括基本动力学性质、正平衡点的存在性、所有平衡点的渐进稳定性、霍普夫分支、分支周期解的方向和稳定性。我们还提供了一些全球性的功能和可能发生的多稳定性在我们的模型。此外，我们进行了详细的数值模拟，以验证我们的数学结果数值。我们的数学和数值结果表明，捕食者的趋性敏感性应小于一定的阈值密度，捕食者可能的生存能力。我们提供了一些敏感性分析，我们的模型解决方案的三个重要的模型参数，即，捕食者的敏感性，恐惧的水平，和捕食者的容忍限度。我们可以观察到捕食者容忍限的扰动对模型动态的影响最大。初始阶段，捕食者趋性敏感性对被捕食者有正的影响，降低了被捕食者的捕杀率;但长期来看，捕食者趋性敏感性对两个种群的解都有负的影响，降低了被捕食者的生长率，从而影响了两个种群的整体适应度。我们的研究结果可能会提供一些有用的生物学见解的捕食者-猎物的相互作用。
We study the dynamics of a prey-predator interaction model that incorporates: (1) reduction of prey growth rate, in the form of fear effect, in presence of predator; and (2) group defense of prey, against predation, by using the Monod-Haldane type functional response. Moreover, we interrelate these two factors, through the predator-taxis sensitivity, as the total time or energy for foraging and defense is constant for prey. If the prey invests more time or energy for group defense, then reproduction may decrease due to that investment. We provide detailed mathematical results, including, basic dynamical properties, existence of positive equilibria, asymptotic stability of all equilibria, Hopf-bifurcation, direction and stability of bifurcated periodic solutions. We also provide some global features and possible occurrence of multi-stability in our model. Furthermore, we perform detailed numerical simulations to validate our mathematical results numerically. Our mathematical and numerical results suggest that the predator-taxis sensitivity should be less than some threshold density, for possible survivability of predator. We provide some sensitivity analysis of our model solutions with respect to the three important model parameters, namely, the predator-taxis sensitivity, level of fear, and the tolerance limit of predator. We can observe that the perturbation of the tolerance limit of predator has the greatest influence over model dynamics. Initially, the predator-taxis sensitivity has a positive effect on prey as its decreases the killing rate, however, for long run, its effect is negative on both the solutions, as it decreases the growth rate of prey, which affects overall fitness of both the populations. Our results may provide some useful biological insights on predator-prey interactions.