We consider the propagation dynamics of a general heterogeneous reaction-diffusion system under a shifting environment. By developing the fixed-point theory for second order non-autonomous differential system and constructing appropriate upper and lower solutions, we show there exists a nondecreasing wave front with the speed consistent with the habitat shifting speed. We further show the uniqueness of forced waves by the sliding method and some analytical skills, and we obtain the global stability of forced waves by applying the dynamical systems approach. Moreover, we establish the spreading speed of the system by appealing to the abstract theory of monotone semiflows. Applications and numerical simulations are also given to illustrate the analytical results.

我们考虑在变化的环境下一般异质反应扩散系统的传播动力学。通过发展二阶非自治微分系统的不动点理论并构建适当的上下解，我们表明存在一个速度与栖息地移动速度一致的非递减波前。我们通过滑动方法和一些分析技巧进一步展示了强迫波的独特性，并通过应用动力系统方法获得了强迫波的全局稳定性。此外，我们通过调用单调半流的抽象理论来建立系统的传播速度。还给出了应用和数值模拟来说明分析结果。