Abstract:  One of the most interesting topics in ecology systems is the stability of species. It is a n-species (one-prey, the others-predator) ratio-dependent predator-prey system with time delay and functional response at the seme time and was studied. By differential inequality constructing suitable Lyapunov functional, a sufficient condition was obtained for the global stability of the positive equilibrium of the system. Finally, the numerical simulation result of population model was given.

Key words: Time delay  , Global stability   , Lyapunov functional   , Species

摘要： 在生态系统中,种群的稳定性一直是研究的重点内容之一,考虑了一个同时具有时滞和功能性反应
的n 种群模型,其中一个为被捕食者,其它的为捕食种群,通过微分不等式和构造合适的Lyapunov泛函给出了解的
有界性和正平衡点全局稳定的充分条件,并给出模型的数值模拟结果。

关键词: 时滞 ,   , 全局稳定  ,   , Lyapunov泛函  ,  ,  种群