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中文摘要：
基于非线性常微分方程泛函分析研究了一类变时滞n维非自治Lotka—Volterra系统周期正解的存在性，利用重合度理论建立了这类系统周期正解的存在性判据，得到了相应的充分性条件．同时对系统的持久性问题也作了分析，得到了相应的定理．最后，通过计算机仿真，对文中论述周期正解的存在性进行了佐证．
英文摘要：
Based on the functional analysis of nonlinear ordinary differential equation, we study a mutualism system of n-dimensional Lotka-Voherra with delays, and with the help of coincidence degree theory, we establish the existence of positive periodic solution of this system. The existence theorem is obtained in this paper, and obtained the corresponding conditions. At the same time, we analyzed the permanence of the system. Finally, Computer simulations are presented to illustrate the conclusions.
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