In this paper, we investigate a delay reaction–diffusion–advection model with ideal free dispersal. The stability of positive steady-state solutions and the existence of the associated Hopf bifurcation are obtained by analyzing the principal eigenvalue of an elliptic operator. By the normal form theory and the center manifold reduction, the stability and bifurcation direction of Hopf bifurcating periodic solutions are obtained. Moreover, numerical simulations and a brief discussion are presented to illustrate our theoretical results.

中文翻译：

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具有理想自由扩散的时滞反应-扩散-对流方程中的Hopf分叉

在本文中，我们研究了具有理想自由扩散的延迟反应-扩散-对流模型。通过分析椭圆算子的本征值，可以得到正稳态解的稳定性以及相关的Hopf分支的存在。利用范式理论和中心流形约简，得到了Hopf分岔周期解的稳定性和分岔方向。此外，数值模拟和简短的讨论被提出来说明我们的理论结果。