This article focus on the Hopf bifurcation of a delayed reaction–diffusion equation with advection term subject to Dirichlet boundary and no-flux boundary conditions in a bounded domain, respectively. It is shown that the existence of spatially non-homogeneous steady-state solutions will be obtained when the parameter $\lambda$ of the model (9) closes to the principle eigenvalue ${\lambda }_1$ of the elliptic operator ${\mathfrak{L}}_{\lambda }$. Moreover, a supercritical Hopf bifurcation occurs near the non-homogeneous positive steady-state at a series critical time delay values. Finally, we elucidate the effect of advection on Hopf bifurcation values. It is worth noting that the advective effect has accelerated the generation of Hopf bifurcation to a certain extent.

本文重点讨论具有对流项的延迟反应-扩散方程的 Hopf 分岔，该方程分别受有界域中的狄利克雷边界和无通量边界条件约束。结果表明，当参数为$\lambda$ 模型(9)的接近于主特征值 ${\lambda }_1$ 椭圆算子的 ${\mathfrak{升}}_{\lambda }$. 此外，超临界 Hopf 分岔发生在非均匀正稳态附近的一系列临界时间延迟值。最后，我们阐明了对流对 Hopf 分岔值的影响。值得注意的是，平流效应在一定程度上加速了Hopf分岔的产生。