This paper is mainly concerned with the forced waves and gap formations for a Lotka–Volterra competition model with nonlocal dispersal and shifting habitats. We first show that there exist two positive numbers $c_1^{\ast }$ and $c_2^{\ast }$ such that the system admits a forced wave provided that the forcing speed $c\in (-c_2^{\ast },c_1^{\ast })$ by the iterative techniques combining with some known results for the forced moving KPP equations. Meanwhile, we use some delicate analysis to obtain the asymptotic behaviors at infinity of the forced waves with nonzero forcing speed $c\in (-c_2^{\ast },0)\cup (0,c_1^{\ast })$. Then, based on the comparison argument, we prove that the gap formations exist for $c>c_1^{\ast }$ and $c<-c_2^{\ast }$. Finally, some numeric simulation results are presented to confirm our theoretical results, which also contains the critical cases of $c=c_1^{\ast }$ and $c=-c_2^{\ast }$.

本文主要涉及具有非局部分散和迁移栖息地的Lotka-Volterra竞争模型的强迫波和间隙形成。我们首先证明存在两个正数$C_{\mathrm{1个}}^{\ast }$ 和 $C_2^{\ast }$ 这样，只要施加速度快，系统就可以接受强制波 $C\in （-C_2^{\ast }，C_{\mathrm{1个}}^{\ast }）$通过迭代技术结合一些已知的强迫KPP方程的结果。同时，我们使用一些精细的分析来获得具有非零强迫速度的强迫波在无穷大处的渐近行为。$C\in （-C_2^{\ast }，0）\cup （0，C_{\mathrm{1个}}^{\ast }）$。然后，基于比较论证，我们证明存在间隙形成$C>C_{\mathrm{1个}}^{\ast }$ 和 $C<-C_2^{\ast }$。最后，提供一些数值模拟结果以证实我们的理论结果，其中还包括以下关键情况：$C=C_{\mathrm{1个}}^{\ast }$ 和 $C=-C_2^{\ast }$。