We study a Lotka–Volterra competition–diffusion model that describes the growth, spread and competition of two species in a shifting habitat. Some results have been obtained previously for some cases for the diffusion rates and competitions rates, and in this paper we continue to explore the remaining complementary case for the spatial dynamics of the system. Our main result in this paper reveals an essential difference between the case of faster diffuser being weak competitor and the case of faster diffuser being strong competitor: with the severe habitat worsening with constant speed, for the former the two competing species can co-persist by spreading, whereas for the latter, co-persistence is impossible.

我们研究了Lotka-Volterra竞争扩散模型，该模型描述了两个物种在不断变化的栖息地中的生长，传播和竞争。先前已经针对扩散率和竞争率的某些情况获得了一些结果，在本文中，我们将继续探索系统空间动力学的其余互补情况。我们在本文中的主要结果揭示了较快的扩散器弱竞争者与较快的扩散器强竞争者之间的本质区别：随着严重栖息地的恶化以恒定的速度恶化，对于前者而言，两个竞争物种可以通过扩散，而对于后者，则不可能持续。