<p>In this paper, the impact of nonlocal fear effect and mutual interference between predators in a diffusive predator–prey model are studied. Previous studies show that the predator’s voice and smell cause more fear in the prey than direct predation. The predator’s voice can transmit over long distances, causing indirect prey fear. Thus, nonlocal fear can make the model more reasonable. Meanwhile, mutual interference between predators is widely present in nature and is an important influencing factor in ecosystem dynamics. Mutual interference and nonlocal fear effect are intertwined and affect the dynamic balance of the predator–prey system, influencing the generation of Hopf bifurcation and Turing instability. Numerically it is shown that different patterns may occur due to parameters related to nonlocal fear, mutual interference, and prey dispersal. First, as the prey diffusion coefficient decreases, stripe patterns become denser. Second, when Turing instability occurs, the spatial structure between predator and prey has transitioned from regular to complex with the increased level of mutual interference between predators, and a high level of fear can produce periodic solutions. Third, when Hopf bifurcation occurs, a high level of fear can exclude periodic solutions to stabilize the model, and adding mutual interference between predators at a certain level of fear (when there is no initial mutual interference) can also achieve it.</p>

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Impact of nonlocal fear effect and mutual interference between predators in a diffusive predator–prey model

  • Chenyu Wang,
  • Wensheng Yang

摘要

In this paper, the impact of nonlocal fear effect and mutual interference between predators in a diffusive predator–prey model are studied. Previous studies show that the predator’s voice and smell cause more fear in the prey than direct predation. The predator’s voice can transmit over long distances, causing indirect prey fear. Thus, nonlocal fear can make the model more reasonable. Meanwhile, mutual interference between predators is widely present in nature and is an important influencing factor in ecosystem dynamics. Mutual interference and nonlocal fear effect are intertwined and affect the dynamic balance of the predator–prey system, influencing the generation of Hopf bifurcation and Turing instability. Numerically it is shown that different patterns may occur due to parameters related to nonlocal fear, mutual interference, and prey dispersal. First, as the prey diffusion coefficient decreases, stripe patterns become denser. Second, when Turing instability occurs, the spatial structure between predator and prey has transitioned from regular to complex with the increased level of mutual interference between predators, and a high level of fear can produce periodic solutions. Third, when Hopf bifurcation occurs, a high level of fear can exclude periodic solutions to stabilize the model, and adding mutual interference between predators at a certain level of fear (when there is no initial mutual interference) can also achieve it.