In this paper, we study a Lotka–Volterra cooperative system with nonlocal dispersal under worsening habitats. By constructing appropriate vector super-/subsolutions combined with the monotone iteration scheme, we obtain the existence of bounded and positive forced waves connecting zero equilibrium to the coexistence state of the limiting system corresponding to the most favorable resource with the wave speed at which the habitat is worsening. Compared with the existence result of traveling wave to the homogeneous system, we find that the wave phenomenon is more likely to occur in such shifting environment. Here, we remove the common assumption that the dispersal kernels are compactly supported and symmetric. Further, we investigate the tail behavior of the forced waves, especially for the rate of convergence to the extinction state, and derive the long-time dynamics of two species. Our result shows that weak interspecies cooperation and nonlocal diffusion pattern cannot prevent species from disappearing eventually under such a worsening habitat.

在本文中，我们研究了在生境恶化的情况下具有非局部扩散的Lotka-Volterra合作系统。通过构造适当的矢量超解/子解并结合单调迭代方案，我们获得了有界和正向强迫波的存在，该强迫波将零平衡连接到与最有利资源相对应的限制系统的共存状态，其中该限制条件与栖息地的波速有关在恶化。与行波到均质系统的存在结果相比，我们发现在这种变化的环境中波现象更容易发生。在这里，我们删除了分散核被紧凑支持和对称的一般假设。此外，我们研究了强迫波的尾部行为，尤其是对于收敛到消光态的速率，并推导出两个物种的长期动力学。我们的结果表明，在这种日益恶化的栖息地下，弱种间合作和非本地扩散模式无法阻止物种最终消失。