Abstract In this work, we introduce a two-dimensional domain predator-prey model with strong Allee effect and investigate the Turing instability and the phenomena of the emergence of patterns. The occurrence of the Turing instability is ensured by the conditions that are procured by using the stability analysis of local equilibrium points. The amplitude equations (for supercritical case cubic Stuart–Landau equation and for subcritical quintic Stuart–Landau equation) are derived appropriate for each case by using the method of multiple time scale and show that the system supports patterns like squares, stripes, mixed-mode patterns, spots and hexagonal patterns. We obtain the asymptotic solutions to the model close to the onset instability based on the amplitude equations. Finally, numerically simulations tell how cross-diffusion plays an important role in the emergence of patterns.

中文翻译：

---

具有强 Allee 效应的二维域中由交叉扩散引起的图灵模式

摘要 在这项工作中，我们引入了一个具有强 Allee 效应的二维域捕食者-猎物模型，并研究了图灵不稳定性和模式出现的现象。图灵不稳定性的发生是通过使用局部平衡点的稳定性分析获得的条件来保证的。振幅方程（超临界情况三次 Stuart-Landau 方程和亚临界五次 Stuart-Landau 方程）通过使用多时间尺度的方法推导出适用于每种情况，并表明系统支持正方形、条纹、混合模式等模式图案、斑点和六边形图案。我们基于振幅方程获得接近起始不稳定性的模型的渐近解。最后，