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山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (7): 30-38.doi: 10.6040/j.issn.1671-9352.0.2018.018

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一类离散宿主-寄生物模型动态研究

刘华1,叶勇1,魏玉梅2*,杨鹏1,马明1,冶建华1,马娅磊1   

  1. 1.西北民族大学数学与计算机科学学院, 甘肃 兰州 730030;2.西北民族大学实验中心, 甘肃 兰州 730030
  • 收稿日期:2018-01-17 出版日期:2018-07-20 发布日期:2018-07-03
  • 作者简介:刘华(1977— ),男,博士,教授,研究方向为生态数学及计算机模拟. E-mail:liuhuaemail@foxmail.com*通信作者简介:魏玉梅(1989— ),女,高级实验师,研究方向为应用生物学. E-mail:649118046@qq.com
  • 基金资助:
    国家自然科学基金资助项目(31260098,11361049,31560127);西北民族大学中央高校基本科研业务费资金资助项目(31920180116,31920180044,31920170072);国家民委中青年英才计划资助项目(〔2014〕121号);甘肃省科技计划项目资助(1610RJZA102);西北民族大学“双一流”和特色发展引导专项资金资助项目;西北民族大学2018年度实验室开放项目(SYSKF-2018225,SYSKF-2018236)

Study of dynamic of a discrete host-parasitoid model

LIU Hua1, YE Yong1, WEI Yu-mei2*, YANG Peng1, MA Ming1, YE Jian-hua1, MA Ya-lei1   

  1. 1. School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China;
    2. The Experiment Center, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Received:2018-01-17 Online:2018-07-20 Published:2018-07-03

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摘要： 通过建立一类具有Allee效应和HollingⅢ型功能反应函数的宿主-寄生物模型,讨论了平衡点的局部稳定性与持久性。通过计算机模拟,以内禀增长率r作为分岔图的参数,模拟Allee效应对模型动态行为的产生的影响。研究结果发现:在同时具有Allee效应和HollingⅢ型功能反应的模型系统中,引入 Allee效应会加速种群走向灭绝,当系统受强Allee效应会减少系统混沌动态。

关键词: HollingⅢ型功能反应, 分岔图, Allee效应, 持久性, 稳定性

Abstract: A host-parasitoid model with Allee effect and Holling Ⅲ functional response function was established, and the local stability and persistence of equilibria was discussed. The influence of the Allee effect on the dynamic behavior of the model is simulated by the computer simulation and the intrinsic growth rate r as the parameter of the bifurcation diagram. We found that the introduction of Allee effect will accelerate the extinction of population in the model with both Allee effect and Holling Ⅲ functional response. When the system is strong Allee, the chaotic dynamics of the system will be reduced.

Key words: stability, persistence, bifurcation diagram, Holling Ⅲ functional response, Allee effect

中图分类号: 

  • O29
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