时滞非自治的捕食者一食饵系统的持续性和全局稳定性

Persistence and Global Stability for Delay Nonautonomous Predator-prey System

为了研究一类没有即时负反馈控制的3种群捕食者-食饵系统的持续性和全局稳定性;在给定的条件下,利用不等式知识,证明了系统的一致持续性.并通过构造lyapunov函数,导出了该系统全局稳定性的充分条件.在Lotka-Volterra模型中,考虑了3个种群——y_1,y_2,y_3;在这里y_2,y_3是捕食者;y_1,y_2是食饵;其中y_2在捕食y_1的同时又被y_3捕食;y_3既捕食y_1,又捕食y_2.

In order to study the uniform persistence and global stability of a delayed nonautonomous three specie predator-prey Lotka-Volterra system without dominating instantaneous negative feedback. In an appropriate condition, using the knowledge of not-equation, we proved the system is uniformly persistent by constructing a suitable Lyapunov function. Sufficient condition are derived form the global stability of the system. The author considered three species y1, y2, Y3 in the system which has two predator y2, y3 and two preys Y1,Y2; Y2 not only is the predator to y1 but also is the prey to Y3, y1 is the prey to y3 too.