一类具有时滞、脉冲效应和阶段结构的捕食者-食饵模型

doi:10.13371/j.cnki.chin.q.j.m.2014.01.007

数学季刊 ›› 2014, Vol. 29 ›› Issue (1): 45-54.doi: 10.13371/j.cnki.chin.q.j.m.2014.01.007

一类具有时滞、脉冲效应和阶段结构的捕食者-食饵模型

1. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College 2. Department of Guns Engineering, Shijiazhuang Mechanical Engineering College

收稿日期:2012-04-08 出版日期:2014-03-30 发布日期:2022-12-12
作者简介:DU Yan-ke(1977-), female, native of Shenzhou, Hebei, a lecturer of Shijiazhuang Mechanical Engineering College, engages in differential equations and mathematical biology.
基金资助:
Supported by the NNSF of China (11071254)； Supported by the Science Foundation of Mechanical Engineering College (YJJXM11004)

A Stage-structured Predator-prey Model with Time Delay and Impulsive Effects

1. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College 2. Department of Guns Engineering, Shijiazhuang Mechanical Engineering College

Received:2012-04-08 Online:2014-03-30 Published:2022-12-12
About author:DU Yan-ke(1977-), female, native of Shenzhou, Hebei, a lecturer of Shijiazhuang Mechanical Engineering College, engages in differential equations and mathematical biology.
Supported by:
Supported by the NNSF of China (11071254)； Supported by the Science Foundation of Mechanical Engineering College (YJJXM11004)

摘要/Abstract

摘要： A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated, in which both the prey and the predator have a history that takes them through two stages: immature and mature. The global attractiveness of the pest-eradication periodic solution is discussed, and sufficient condition is obtained for the permanence of the system. Further, numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.

关键词: stage-structure, delay, biological and chemical control, impulsive effect, global attractiveness, permanence

Abstract: A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated, in which both the prey and the predator have a history that takes them through two stages: immature and mature. The global attractiveness of the pest-eradication periodic solution is discussed, and sufficient condition is obtained for the permanence of the system. Further, numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.

Key words: stage-structure, delay, biological and chemical control, impulsive effect, global attractiveness, permanence

中图分类号:

O175.1

杜艳可, 吴向东, 徐瑞. 一类具有时滞、脉冲效应和阶段结构的捕食者-食饵模型[J]. 数学季刊, 2014, 29(1): 45-54.

DU Yan-ke, WU Xiang-dong, XU Ru. A Stage-structured Predator-prey Model with Time Delay and Impulsive Effects[J]. Chinese Quarterly Journal of Mathematics, 2014, 29(1): 45-54.

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一类具有时滞、脉冲效应和阶段结构的捕食者-食饵模型

A Stage-structured Predator-prey Model with Time Delay and Impulsive Effects

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