In this paper, we study the spatial dynamics of the lattice Lotka–Volterra competition system in a shifting habitat. First, we discuss the corresponding ranges of the environmental worsening speed $c$ in the following three cases: (a) both species are extinct; (b) one species is extinct, the other is persistent; (c) both species are persistent. Moreover, for species persistence, it is achieved by diffusing to the favorable habitat with certain speeds. Finally, some estimates of these speeds are given.

中文翻译：

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在变化的栖息地中格子Lotka-Volterra竞争系统的空间动力学

在本文中，我们研究了在变化的栖息地中的Lotka–Volterra竞争系统的空间动力学。首先，我们讨论环境恶化速度的相应范围$C$在以下三种情况下：（a）两种物种均已灭绝；（b）一个物种已灭绝，另一物种已灭绝；（c）这两个物种都是持久性的。此外，对于物种的持久性，可以通过以一定速度扩散到有利的栖息地来实现。最后，给出了这些速度的一些估计。