Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India.
Department of Mathematics Education, Catholic University of Daegu, Gyeongsan, Gyeongbuk 712-702, South Korea.
Chaos. 2021 Mar;31(3):033128. doi: 10.1063/5.0035130.
Population distribution of interacting species in a large scale natural system is heterogeneous and subject to change for various reasons. Here, we explore how behavioral modification in prey species due to fear of predator and mutual interference between predators can create different spatiotemporal patterns in population distribution. We show that the fear factor and diffusion in a ratio-dependent predator-prey model may show more complex dynamics than observed earlier. It is shown that when prey diffusivity is low, prey remains concentrated at different patches throughout the domain. However, prey density becomes low at the patches as they disperse at a higher rate. Mixed and stripe patterns are observed during the transition from a hot spot pattern at the lower prey diffusivity to a cold spot pattern at its higher value. Pattern transition is, however, completely opposite if the antipredator behavior is gradually increased. Our simulation results reveal that the spatiotemporal chaotic pattern may also be observed in the Hopf-Turing region of instability provided prey shows a higher level of antipredator behavior. The chaotic pattern of the Hopf-Turing region may be shifted to a spot type pattern of the Turing region depending on the refuge level of the habitat.
在大规模自然系统中，相互作用的物种的种群分布是不均匀的，并可能由于各种原因发生变化。在这里，我们探讨了由于对捕食者的恐惧和捕食者之间的相互干扰而导致猎物物种行为发生变化，如何在种群分布中产生不同的时空模式。我们表明，基于比例的捕食者-猎物模型中的恐惧因素和扩散可能表现出比以前观察到的更复杂的动力学。结果表明，当猎物扩散率较低时，猎物会在整个区域的不同斑块中集中存在。然而，当它们以更高的速率扩散时，斑块中的猎物密度会降低。在从较低猎物扩散率下的热点模式到较高值下的冷点模式的转变过程中，观察到混合和条纹模式。然而，如果逐渐增加反捕食者行为，则模式转变是完全相反的。我们的模拟结果表明，如果猎物表现出更高水平的反捕食者行为，则在不稳定性的 Hopf-Turing 区域也可能观察到时空混沌模式。混沌模式的 Hopf-Turing 区域可能会根据栖息地的避难所水平转移到 Turing 区域的点状模式。
