一类带有HollingⅡ类功能性反应和相互干扰及脉冲效应的捕食系统

数学季刊 ›› 2008, Vol. 23 ›› Issue (4): 480-490.

一类带有HollingⅡ类功能性反应和相互干扰及脉冲效应的捕食系统

1. Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China2. College of Mathematics and Information Science,Xinyang Normal University,Xinyang 464000,China3. Department of Mathematics,Huanghuai University,Zhumadian 463000,China

收稿日期:2006-04-10 出版日期:2008-12-30 发布日期:2023-09-13
作者简介:GUO Hong-jian(1972-), male, native of Weishi, Henan, an associate professor of Xinyang Normal University, M.S.D., engages in biomathematics; SONG Xin-yu(1961-), male, native of Huangcbuan, Henan, a professor of Xinyang Normal University, Ph.D., engages in dynamical systems, biomathematics.
基金资助:
Supported by the National Natural Science Foundation of China(10771179)； Supported by the Natural Science Foundation of the Education Department Henan Province(20071 10028)；

A Kind of Predator-prey System of Holling Type II and Interaction Perturbation with Impulsive Effect

1. Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China2. College of Mathematics and Information Science,Xinyang Normal University,Xinyang 464000,China3. Department of Mathematics,Huanghuai University,Zhumadian 463000,China

Received:2006-04-10 Online:2008-12-30 Published:2023-09-13
About author:GUO Hong-jian(1972-), male, native of Weishi, Henan, an associate professor of Xinyang Normal University, M.S.D., engages in biomathematics; SONG Xin-yu(1961-), male, native of Huangcbuan, Henan, a professor of Xinyang Normal University, Ph.D., engages in dynamical systems, biomathematics.
Supported by:
Supported by the National Natural Science Foundation of China(10771179)； Supported by the Natural Science Foundation of the Education Department Henan Province(20071 10028)；

摘要/Abstract

摘要： A kind of predator-prey system of Holling typeⅡ and interaction perturbation with impulsive effect is presented. By using Floquet theory and small amplitude perturbations skills, the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively. Finally, the existence of positive periodic solution is investigated by the bifurcation theory.

关键词: predator-prey system, periodic solution, threshold, asymptotically stable, im- pulsive effect, extinction, permanence

Abstract: A kind of predator-prey system of Holling typeⅡ and interaction perturbation with impulsive effect is presented. By using Floquet theory and small amplitude perturbations skills, the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively. Finally, the existence of positive periodic solution is investigated by the bifurcation theory.

Key words: predator-prey system, periodic solution, threshold, asymptotically stable, im- pulsive effect, extinction, permanence

中图分类号:

O175

郭红建, 赵中, 宋新宇等. 一类带有HollingⅡ类功能性反应和相互干扰及脉冲效应的捕食系统[J]. 数学季刊, 2008, 23(4): 480-490.

GUO Hong-jian, ZHAO Zhongl, SONG Xin-yu, CHEN Lan-sun. A Kind of Predator-prey System of Holling Type II and Interaction Perturbation with Impulsive Effect [J]. Chinese Quarterly Journal of Mathematics, 2008, 23(4): 480-490.

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