Global dynamics of a diffusive competitive Lotka–Volterra model with advection term and more general nonlinear boundary condition

Abstract We investigate a competitive diffusion–advection Lotka–Volterra model with more general nonlinear boundary condition. Based on some new ideas, techniques, and the theory of the principal spectral and monotone dynamical systems, we establish the influence of the following parameters on the dynamical behavior of system (1. 2): advection rates ₔ α u and ₕ α v, interspecific competition intensities cₔ c u and cₕ c v, the resources functions rₔ r u and rₕ r v of the two competitive species, and nonlinear boundary functions g₁ g 1 and g₂ g 2. The models of (Tang and Chen in J. Differ. Equ. 269 (2): 1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264: 4176–4198, 2018) are particular cases of our results when g₈ const g i ≡ c o n s t for i=1, 2 i = 1, 2, and hence this paper extends some of the conclusions from (Tang and Chen in J. Differ. Equ. 269 (2): 1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264: 4176–4198, 2018).