In this paper, we consider two species chemotaxis systems with Lotka–Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number $c^{\ast }$. We also show the non-existence of such traveling waves with speed less than some critical number $c_0^{\ast }$, which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring $c^{\ast }=c_0^{\ast }$, which implies that the minimum wave speed exists and is not affected by the chemoattractant.

在本文中，我们考虑具有 Lotka-Volterra 竞争反应项的两个物种趋化系统。在这样一个系统中的参数的适当条件下，我们建立连接两个波速大于某个临界数的空间均匀平衡解的系统的行波解的存在性$C^{＊}$. 我们还表明不存在这种速度小于某个临界数的行波$C_0^{＊}$，这与趋化性无关。此外，在反应项系数的适当假设下，我们获得了趋化敏感性系数的明确范围，确保$C^{＊}=C_0^{＊}$，这意味着存在最小波速并且不受化学引诱剂的影响。