文章摘要
引用本文:陈江彬.具避难所的捕食者-食饵系统的定性研究[J].福州大学学报(自然科学版),2014,42(6):812~818
具避难所的捕食者-食饵系统的定性研究
Qualitative analysis of a prey-predator model incorporating a prey refuge
  
DOI:10.7631/issn.1000-2243.2014.06.0812
中文关键词: Hopf分支  极限环  避难所  捕食者-食饵系统
英文关键词: Hopf bifurcation  limit cycle  refuge  predator-prey system
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作者单位
陈江彬 福州大学至诚学院福建 福州 350002 
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中文摘要:
      研究具有Holling-II功能反应函数的捕食者-食饵系统. 运用Poincaré形式级数法,得到系统正平衡点至多是一阶稳定细焦点. 通过定性研究得到系统的正解有界,并且当平衡点不稳定时,系统存在唯一稳定的极限环. 最后,利用计算机进行数值模拟,验证了所得结论.
英文摘要:
      A predator-prey system with Holling-II response function incorporating a prey refuge is investigated. By using the method of formal power series of Poincaré,we get a result that the positive equilibrium is a stable fine-focus of order at most 1. The qualitative analysis for the model indicates that the positive solutions of the system are all bounded,thus,when the equilibrium is unstable,the system has exactly one stable limit cycle. Some computer simulations are presented to illustrate the conclusions.
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