一类双斑块Lotka-Volterra型捕食模型

数学季刊 ›› 2011, Vol. 26 ›› Issue (4): 475-487.

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一类双斑块Lotka-Volterra型捕食模型

Institute of Applied Mathematics, Ordnance Engineering College

收稿日期:2008-01-20 出版日期:2011-12-30 发布日期:2023-04-12
作者简介:WANG Li-li(1977-), female, native of Botou, Hebei, a lecturer of Ordnance Engineering College, M.S.D., engages in biomathematics; XU Rui(1962-), male, native of Zhangjiakou, Hebei, a professor of Ordnance Engineering College, Ph.D., engages in biomathematics.
基金资助:
Supported by the National Natural Science Foundation of China(10471066)； Supported by the Ordnance Engineering College Foundation(YJJXM05013)

A Lotka-Volterra Type Predator-prey Model in a Two-patchy Environment

Institute of Applied Mathematics, Ordnance Engineering College

Received:2008-01-20 Online:2011-12-30 Published:2023-04-12
About author:WANG Li-li(1977-), female, native of Botou, Hebei, a lecturer of Ordnance Engineering College, M.S.D., engages in biomathematics; XU Rui(1962-), male, native of Zhangjiakou, Hebei, a professor of Ordnance Engineering College, Ph.D., engages in biomathematics.
Supported by:
Supported by the National Natural Science Foundation of China(10471066)； Supported by the Ordnance Engineering College Foundation(YJJXM05013)

摘要/Abstract

摘要： In this paper, a Lotka-Volterra type predator-prey model with time delays due to gestation of the predator and dispersal for both the prey and the predator is investigated. We first establish two different results on the permanence of the system. Using coincidence degree theory, sufficient conditions are derived for the existence of positive periodic solutions, and by constructing an appropriate Lyapunov functional, we further discuss their uniqueness and global stability. Numerical simulations are carried out to illustrate the main results.

关键词: delay, dispersal, periodic solution, global stability

Abstract: In this paper, a Lotka-Volterra type predator-prey model with time delays due to gestation of the predator and dispersal for both the prey and the predator is investigated. We first establish two different results on the permanence of the system. Using coincidence degree theory, sufficient conditions are derived for the existence of positive periodic solutions, and by constructing an appropriate Lyapunov functional, we further discuss their uniqueness and global stability. Numerical simulations are carried out to illustrate the main results.

Key words: delay, dispersal, periodic solution, global stability

中图分类号:

O175.13

王丽丽, 徐瑞. 一类双斑块Lotka-Volterra型捕食模型[J]. 数学季刊, 2011, 26(4): 475-487.

WANG Li-li, XU Rui. A Lotka-Volterra Type Predator-prey Model in a Two-patchy Environment[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(4): 475-487.

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一类双斑块Lotka-Volterra型捕食模型

A Lotka-Volterra Type Predator-prey Model in a Two-patchy Environment

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