辽宁石油化工大学学报

辽宁石油化工大学学报 ›› 2011, Vol. 31 ›› Issue (1): 61-63.DOI: 10.3696/j.issn.1672-6952.2011.01.017

• 数学与管理 • 上一篇    下一篇

一类三种群食物链模型的混沌行为

滕 勇   

  1. 沈阳工业大学辽阳校区,辽宁辽阳111000
  • 收稿日期:2010-07-15 出版日期:2011-03-25 发布日期:2017-07-05
  • 作者简介:滕勇(1968-),男,辽宁丹东市,副教授。
  • 基金资助:
    辽宁省教育厅普通高等学校科研计划项目
    (L2010408

Chaos in a Three Species Food Chain

 

TENG Yong
  

  1. Liaoyang Campus, Shenyang University of Technology, Liaoyang Liaoning 111000,P.R. China
  • Received:2010-07-15 Published:2011-03-25 Online:2017-07-05

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摘要： 生态学中的混沌现象是一个重要的研究方向,它反映了生物种群数量在吸引子中做复杂的运动,各
种群数量处于混沌状态。建立了一个具有HollingⅡ型功能性反应的三种群食物链模型,利用微分不等式得到了种
群的有界性;采用数值模拟的手段对该三种群模型进行了定量的分析,得到了的不同参数情况下的相空间轨迹,并
通过分岔图说明系统随着参数变化而呈现出不同的状态,系统从单周期极限环,经倍周期现象,最后呈现出混沌状
态,在自然界的食物网中混沌运动是普遍的。

关键词: 种群 ,  ,  , 食物链 ,  ,  , 混沌 ,  ,  , 分岔 ,  , 吸引子

Abstract: Chaos is an important research direction in ecology and the number of species in a chaotic state has complex movements in strange attractor. The three species ratio dependent food chain model with Holling Ⅱ functional response was established. The boundedness of species was obtained by differential inequality. The quantitative analysis of the three species food chain model was investigated by numerical simulations and the existence of chaotic dynamic was studied by the bifurcation diagrams. The strange attractor was obtained for suitable choice of parametric values and is existence via double periods. The appearance of chaos in this model suggests that chaotic dynamics may be common in natural food webs.

Key words: Species  ,  , Food chain  ,  Chaos,  , Bifurcation ,  , Attractor

引用本文

滕 勇. 一类三种群食物链模型的混沌行为[J]. 辽宁石油化工大学学报, 2011, 31(1): 61-63.

TENG Yong. Chaos in a Three Species Food Chain[J]. Journal of Liaoning Petrochemical University, 2011, 31(1): 61-63.

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