This paper is devoted to investigating the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the techniques of weighted energy method and the comparison principle, we show that all solutions of the Cauchy problem for the discrete diffusive systems converge exponentially to the traveling wave fronts when the initial perturbations around the wave fronts lie in a suitable weighted Sobolev space. Our main results can be extended to more general discrete diffusive systems. We also apply them to the discrete epidemic model with the Holling-II-type and Richer-type effects.

本文致力于研究一类两分量离散扩散系统的波传播及其稳定性。我们首先确定正单调单稳态行波阵面的存在。然后，运用加权能量方法和比较原理，我们证明了当离散波扩散系统的柯西问题的所有解都在合适的加权Sobolev空间中时，所有波前的扰动都以指数形式收敛到行波前。 。我们的主要结果可以扩展到更通用的离散扩散系统。我们还将它们应用于具有Holling-II型和Richer型效应的离散流行病模型。