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 \(\alpha _{u}\) and \(\alpha _{v}\), interspecific competition intensities \(c_{u}\) and \(c_{v}\), the resources functions \(r_{u}\) and \(r_{v}\) of the two competitive species, and nonlinear boundary functions \(g_{1}\) and \(g_{2}\). 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 \(g_{i}\equiv const\) for \(i=1,2\), 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).