中文摘要：

主要研究带Lotka-Volterra互惠源项的多种群趋化模型的唯一正平衡点的稳定性．首先应用非奇M-矩阵理论给出该模型存在唯一正平衡点的充分条件；然后用线性化方法分析正平衡点的局部稳定性；最后结合该模型与一个相应的常微分方程组之间的关系讨论正平衡点的全局渐近稳定性．

英文摘要：

In this paper, we mainly study the stability of a unique positive equi- librium point for a multi-species chemotaxis model with Lotka-Volterra cooperative source. Firstly, we give a sufficient condition to guarantee the existence and unique- ness of positive equilibrium point in the model by applying the nonsingular M-matrix theory. Then, by using the linearization, the local stability of the unique positive equi- librium point is proved. Finally, we discuss the global asymptotical stability of the positive equilibrium point by the relationship between this model and a corresponding system of ordinary differential equations.