In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered. The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis. The technique of multiple time scales is employed to deduce the amplitude equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter. The stability analysis of these amplitude equations leads to the identification of various Turing patterns driven by the cross-diffusion, which are also investigated through numerical simulations.

中文翻译：

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具有恐惧和群体防御的捕食者—食饵系统中的交叉扩散驱动不稳定性

本文考虑了一种具有食饵对食饵种群和群体防御的恐惧反应的反应扩散食饵－捕食者系统。交叉扩散驱动的不稳定性的发生条件通过线性稳定性分析获得。通过选择交叉扩散系数作为分叉参数，采用多尺度技术推导图灵分叉阈值附近的振幅方程。这些振幅方程的稳定性分析导致了由交叉扩散驱动的各种图灵模式的识别，并通过数值模拟对其进行了研究。