In this paper, we are concerned with the dynamics of a class of two-species reaction–diffusion–advection competition models with time delay subject to the homogeneous Dirichlet boundary condition or no-flux boundary condition in a bounded domain. The existence of steady state solution is investigated by means of the Lyapunov–Schmidt reduction method. The stability and Hopf bifurcation at the spatially nonhomogeneous steady-state are obtained by analyzing the distribution of the associated eigenvalues. Finally, the effect of advection on Hopf bifurcation is explored, which shows that with the increase of convection rate, the Hopf bifurcation phenomenon is more likely to emerge.

在本文中，我们关注一类具有时滞且在有界域中的齐次Dirichlet边界条件或无通量边界条件下的带有时滞的两类反应-扩散-对流竞争模型的动力学。借助Lyapunov–Schmidt约简方法研究了稳态解的存在性。通过分析相关特征值的分布，可以获得在空间非均匀稳态下的稳定性和Hopf分支。最后，探讨了对流对霍普夫分叉的影响，表明随着对流速率的增加，霍普夫分叉现象更容易出现。