In this paper, we consider a diffusive predator–prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spectrum. Delay-induced Hopf bifurcation is also investigated. By utilizing the normal form method and center manifold reduction for partial functional differential equations, the formulas for determining the property of Hopf bifurcation are given.

中文翻译：

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具时滞毒性的扩散性捕食被捕食模型的时延诱发霍普夫分歧。

在本文中，我们考虑具有时滞和猎物毒性的扩散捕食者－食饵模型。通过分析特征值谱，研究了时间延​​迟对正平衡稳定性的影响。还研究了延迟引起的Hopf分叉。通过对部分泛函微分方程采用正规形式法和中心流形约简，给出了确定Hopf分岔性质的公式。