We investigate a reaction–diffusion–advection system which characterizes the interactions between the predator and prey in advective environments, such as streams or rivers. In contrast with non-advective environments, the dynamics of this system is more complicated. It turns out that there exists a critical mortality rate of the predator and two critical advection rates, which classify the dynamic behavior of this system into two or three scenarios, that is, (i) both populations go extinct; (ii) the predator can not invade and the prey survives in the long run; (iii) the predator can invade successfully when rare and it will coexist permanently with the prey. Specially, the predator can invade successfully when rare if both the mortality rate of the predator and the advection rate are suitably small. Furthermore, by the global bifurcation theory and some auxiliary techniques, the existence and uniqueness of coexistence steady states of this system are established. Finally, by means of numerical simulations, the effects of diffusion on the dynamics of this system are investigated. The numerical results show that the random dispersals of both populations favor the invasion of the predator.

我们研究了一种反应-扩散-对流系统，该系统表征了在对流环境（例如河流或河流）中捕食者与被捕食者之间的相互作用。与非平流环境相比，该系统的动力学更为复杂。事实证明，存在捕食者的临界死亡率和两个临界对流率，它们将该系统的动态行为分为两种或三种情况，即：（i）两种种群都灭绝了；（ii）掠夺者无法入侵，并且从长远来看猎物仍然可以生存；（iii）捕食者在稀有情况下可以成功入侵，并将与猎物永久共存。特别地，如果捕食者的死亡率和对流率都适当小，则捕食者在罕见的情况下可以成功入侵。此外，利用全局分岔理论和一些辅助技术，确定了该系统并存稳态的存在性和唯一性。最后，通过数值模拟，研究了扩散对系统动力学的影响。数值结果表明，这两个种群的随机分散有利于捕食者的入侵。