具有无限时滞离散的Predator-Prey系统周期正解的存在性

journal6 ›› 2003, Vol. 24 ›› Issue (2): 52-56.

具有无限时滞离散的Predator-Prey系统周期正解的存在性

(1.吉首大学数学与计算机科学系，湖南吉首 416000；2.湖南大学数学与计量经济学院，湖南长沙 410082)

出版日期:2003-06-15 发布日期:2012-11-07
作者简介:蒋利群(1976-)，女，湖南永州人，湖南大学数学与计量经济学院硕士研究生，吉首大学数学与计算机科学系讲师，主要研究差分方程及其应用.

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

(1.Dept.of Math.And Computer Science,Jishou University,Jishou 416000,Hunan China;2.College of Math.and Econometrics,Hunan University,Changsha 410082,Hunan China)

Online:2003-06-15 Published:2012-11-07

摘要/Abstract

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)r-1a-32-r-3a-12ｅｘｐ（2r-2ω）＞0；（ⅱ）r-1a-32-r-3a-12ｅｘｐ（2r-2ω）-r-2a-11a-32ｅｘｐ（2r-1ω）＜0；（ⅲ）-a-32a-12r-1＋a-32a-11r-2＋a-21a-12r-3＜0．

关键词： Predator-Prey系统, 正周期解, 无限时滞, 离散的, 拓扑度

Abstract: 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)r-1a-32-r-3a-12ｅｘｐ（2r-2ω）＞0；（ⅱ）r-1a-32-r-3a-12ｅｘｐ（2r-2ω）-r-2a-11a-32ｅｘｐ（2r-1ω）＜0；（ⅲ）-a-32a-12r-1＋a-32a-11r-2＋a-21a-12r-3＜0．

Key words: Predator-Prey system, positive periodic solution, infinite delays, discrete, topologic degree

蒋利群, 莫宏敏. 具有无限时滞离散的Predator-Prey系统周期正解的存在性[J]. journal6, 2003, 24(2): 52-56.

JIANG Li-Qun, MO Hong-Min. Existence of Positive Periodic Solutions of Discrete Predator-Prey System With Infinite Delays[J]. journal6, 2003, 24(2): 52-56.