This paper explores the suitability of space fractional-order reaction–diffusion scenarios to model some emergent pattern formation in predator–prey models. Such fractional reaction–diffusion equations are obtained on the basis of a continuous-time random walk approach with spatial memory and local kinetic reaction. The classical space second-order derivative is changed by the fractional Laplacian case. We employ the Fourier spectral method to numerically approximate the fractional Laplacian and advance in time with the novel ETDRK4 method. In other to obtain guidelines on the correct choice of parameters when numerically simulating the full reaction–diffusion models, the local dynamics of the systems are considered. The biological wave scenarios of solutions are verified by presenting some numerical results in two dimensions to mimic some spatiotemporal dynamics such as spots, stripes and spiral patterns which has a lot of ecological implications.

本文探讨了空间分数阶反应 - 扩散场景对捕食者 - 猎物模型中的一些紧急模式形成进行建模的适用性。这种分数反应扩散方程是基于具有空间记忆和局部动力学反应的连续时间随机游走方法获得的。经典空间二阶导数由分数拉普拉斯情况改变。我们采用傅立叶谱方法在数值上近似分数拉普拉斯算子，并使用新颖的 ETDRK4 方法及时推进。为了在数值模拟全反应扩散模型时获得正确选择参数的指南，系统的局部动力学被考虑在内。