Kim Kwangjoong, Choi Wonhyung
College of General Education, Kookmin University, 77, Jeongneung-ro, Seoul, 02707, Korea.
Industry-Academic Cooperation Foundation, Kookmin University, 77, Jeongneung-ro, Seoul, 02707, Korea.
Math Biosci Eng. 2020 Sep 30;17(6):6737-6755. doi: 10.3934/mbe.2020351.
In this paper, we study the effect of directional dispersal of a predator on a predator- prey model. The prey is assumed to have traits making it undetectable to the predator and difficult to chase the prey directly. Directional dispersal of the predator is described when the predator has learned the high hunting efficiency in certain areas, thereby dispersing toward these areas instead of directly chasing the prey. We investigate the stability of the semi-trivial solution and the existence of a coexistence steady-state. Moreover, we show that the predator that moves toward a high-predation area may make the predators survive under the condition the predators cannot survive when they disperse randomly. The results are obtained through eigenvalue analysis and fixed-point index theory. Finally, we present the numerical simulation and its biological interpretations based on the obtained results.
在本文中，我们研究了捕食者的定向扩散对捕食-食饵模型的影响。假设猎物具有一些特征，使其对捕食者不可察觉，并且难以直接追捕。当捕食者了解到在某些区域具有较高的捕猎效率时，就会出现捕食者的定向扩散，从而向这些区域扩散，而不是直接追捕猎物。我们研究了半平凡解的稳定性和共存稳态的存在性。此外，我们表明，向高捕食区域移动的捕食者可能会使捕食者在随机扩散时无法生存的条件下存活下来。结果是通过特征值分析和不动点指数理论得到的。最后，我们根据所得结果给出了数值模拟及其生物学解释。
