具有无限时滞离散的Predator-Prey系统周期正解的存在性  

Existence of Positive Periodic Solutions of Discrete Predator-Prey System With Infinite Delays

作　　者：蒋利群[1] 莫宏敏[1] 

机构地区：[1]吉首大学数学与计算机科学系

出　　处：《吉首大学学报（自然科学版）》2003年第2期52-56,共5页Journal of Jishou University(Natural Sciences Edition)

摘　　要：研究了具有三个物种周期的Predator-Prey差分模型,用拓扑度理论讨论了具有无限时滞差分系统的周期正解的存在性,证明了具有无限时滞差分系统的正周期解存在的充分条件为:(ⅰ) r1 a32- r3 a12exp(2 r2ω)>0;(ⅱ) r1 a32- r3 a12exp(2 r2ω)- r2 a11 a32exp(2 r1ω)<0;(ⅲ)- a32 a12 r1+ a32 a11 r2+ a21 a12 r3<0.The differential model of periodic Predator-Prey with three species is studied.The existence of positive periodic solution of this system with infinite delays is discussed by using the topologic theory.It is proved that the ample conditions for the existence of positive periodic solution of this system are as follows:(ⅰ)132-312exp(22ω)>0;(ⅱ)132-312exp(22ω)-21132exp(21ω)<0;(ⅲ)-32121+32112+21123<0.

关 键 词：物种周期 Predator-prey差分模型 拓扑度理论 无限时滞差分系统 充分条件 正周期解 

分 类 号：O175.7[理学—数学] O189.11[理学—基础数学]