We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka–Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed $c^{⁎}$ such that for each wave speed $c⩽c^{⁎}$, there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed $c<c^{⁎}$ are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves for nonzero speed $c>c^{⁎}$.

我们研究了周期性扩散 Lotka-Volterra 竞争系统的时间周期性行波解的存在性、唯一性和渐近稳定性。在一定条件下，我们证明存在最大波速$C^{⁎}$ 使得对于每个波速 $C⩽C^{⁎}$，存在连接相应动力学系统的两个半平凡周期解的时间周期行波。结果表明，这种行波是唯一的模平移，并且相对于其共同移动坐标系是单调的。我们还表明，具有波速的行波解$C<C^{⁎}$在某种意义上是渐近稳定的。此外，我们建立了非零速度的时间周期行波不存在$C>C^{⁎}$.