In this paper, we investigate a diffusive logistic equation with non-zero Dirichlet boundary condition and two delays. We first exclude the existence of positive heterogeneous steady states, which implies the uniqueness of constant positive steady state. Then, we analyze the local stability and local Hopf bifurcation at the positive steady state. We show that multiple delays can induce multiple stability switches. Furthermore, we prove global stability of the positive steady state under certain conditions and obtain global Hopf bifurcation results. Our theoretical results are illustrated with numerical simulations.

中文翻译：

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具有两个时滞的扩散Logistic人口模型的Dirichlet问题

本文研究具有非零Dirichlet边界条件和两个时滞的扩散逻辑方程。我们首先排除正异质稳态的存在，这意味着恒定正稳态的唯一性。然后，我们分析了正稳态下的局部稳定性和局部Hopf分支。我们表明，多个延迟可以诱发多个稳定性开关。此外，我们证明了在某些条件下正稳态的全局稳定性，并获得了全局Hopf分叉结果。我们的理论结果通过数值模拟得到了说明。