Global dynamics of a Lotka-Volterra competition-diffusion system with nonlinear boundary conditions

Abstract

In this paper, a Lotka-Volterra competition-diffusion system subject to nonlinear boundary conditions is considered with an aim to understand the nonlinear balance between two competing nonlinear mechanisms (namely, interior reaction and boundary flux). A complete picture on the global dynamics (including the existence, nonexistence, global stability, and steady-state bifurcation of semi-trivial positive steady-state solutions) has been studied in terms of inter-specific competition coefficients, the growth rate functions, and boundary reaction functions. Our results extend largely the relevant results in the existing literature on Lotka-Volterra competition-diffusion systems, even those with homogeneous boundary conditions.