In this paper, we propose a predator–prey model with herd behavior and prey-taxis. Then, we analyze the stability and bifurcation of the positive equilibrium of the model subject to the homogeneous Neumann boundary condition. By using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of stable nonconstant solutions bifurcating from the positive equilibrium. Our results show that prey-taxis can yield the occurrence of spatial patterns.

中文翻译：

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具有种群行为，二次死亡率和捕食性的捕食者－被捕食模型中的图灵－霍夫分叉

在本文中，我们提出了一种具有群体行为和捕食性的捕食者－猎物模型。然后，我们分析了模型在齐次Neumann边界条件下的正平衡的稳定性和分支。通过使用抽象的分叉理论，并以食饵-战术敏感性系数作为分叉参数，我们得到了一个由正平衡分叉的稳定的非恒定解的分支。我们的结果表明，猎物出租车可以产生空间格局。