Wave speed selection of a Lotka–Volterra competition system with hybrid dispersals and seasonal succession

In this paper, we propose a new Lotka–Volterra competition system with hybrid dispersals and seasonal succession. Specifically, we assume that the species enter the ecological cycle in favorable season and end in unfavorable season in contrast to models where entry occurs in unfavorable season first. We investigate the minimal wave speed (critical speed) for this new system by upper and lower solution method. Conditions on the model parameters are obtained so that the minimal wave speed is linearly selected or nonlinearly selected. Our result indicates that, if the nonlocal dispersal strength is small, or the kernel is close to the delta function (not fat-tailed), the critical speed is most likely to be linearly selected. As applications, we observe that our result can recover those on the Lotka–Volterra competition system with hybrid dispersals but without seasonal succession.