In this paper, we propose a diffusive predator–prey model with two delays, i.e., a spatial memory delay and a toxic effect delay. Initially, we analyze the global existence of the solution of the system. We then analyze the equilibria’s local stability without delays and investigate the Hopf bifurcation induced by one delay. Subsequently, we establish an analytical framework for constructing the stability switching curve in the delay space. Finally, we present numerical simulations to validate the theoretical results and verify the emergence of various spatial patterns in the system.

中文翻译：

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具有空间记忆和毒素的延迟扩散捕食者-被捕食者模型的分叉分析

在本文中，我们提出了一种具有两个延迟的扩散捕食者-猎物模型，即空间记忆延迟和毒性效应延迟。首先，我们分析系统解的全局存在性。然后，我们分析了无延迟情况下平衡的局部稳定性，并研究了一次延迟引起的 Hopf 分岔。随后，我们建立了一个分析框架来构建延迟空间中的稳定性切换曲线。最后，我们提出数值模拟来验证理论结果并验证系统中各种空间模式的出现。