This paper is concerned with the dynamics of a two-species reaction–diffusion–advection competition model subject to the no-flux boundary condition in a bounded domain. By the signs of the associated principal eigenvalues, we derive the existence and local stability of the trivial and semi-trivial steady-state solutions. Moreover, the nonexistence and existence of the coexistence steady-state solutions stemming from the two boundary steady states are obtained as well. In particular, we describe the feature of the coincidence of bifurcating coexistence steady-state solution branches. At the same time, the effect of advection on the stability of the bifurcating solution is also investigated, and our results suggest that the advection term may change the stability. Finally, we point out that the methods we applied here are mainly based on spectral analysis, perturbation theory, comparison principle, monotone theory, Lyapunov–Schmidt reduction, and bifurcation theory.

本文关注的是在有界域内无通量边界条件下的两种种群反应－扩散－对流竞争模型的动力学。通过相关的本征特征值的符号，我们得出平凡和半平凡稳态解的存在性和局部稳定性。此外，还获得了源于两个边界稳态的共存稳态解的不存在和存在。特别是，我们描述了分叉共存稳态解分支的重合特征。同时，还研究了平流对分叉溶液稳定性的影响，我们的结果表明平流项可能改变稳定性。最后，