Advanced Search
Volume 42 Issue 10
Oct.  2016
Turn off MathJax
Article Contents
Journal of Beijing University of Aeronautics and Astronautics  > 2016  >  42(10): 2075-2081.
LI Ya, HU Hanyan, LIN Junyiet al. Qualitative analysis of a food chain model with alternative prey[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(10): 2075-2081. doi: 10.13700/j.bh.1001-5965.2015.0642(in Chinese)
Citation: LI Ya, HU Hanyan, LIN Junyiet al. Qualitative analysis of a food chain model with alternative prey[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(10): 2075-2081. doi: 10.13700/j.bh.1001-5965.2015.0642(in Chinese)
shu

Qualitative analysis of a food chain model with alternative prey

doi: 10.13700/j.bh.1001-5965.2015.0642
  • 1.

    School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

  • 2. School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT27NZ, United Kingdom

  • 3. School of Mathematics, Peking University, Beijing 100871, China

Funds:  the Fundamental Research Funds for the Central Universities (30361201,30458701)
  • Received Date: 28 Sep 2015
  • Publish Date: 20 Oct 2016
    Abstract
  • Studies in ecology show that alternative prey has important effects on predator-prey system in the aspects of system stability, species persistence, etc. For species at the intermediate level of a food chain, they are prey of top predators, while predating the bottom prey at the same time. Therefore, the effect of changes in intermediate predators' population on the system cannot be ignored. We set up a three-dimensional food chain model composed of top predator, intermediate predator and prey, assuming that the intermediate predator had alternative choice of prey. The existence and stability of the equilibria were derived through dynamical study of the system. The existence of Hopf bifurcation was explored in depth. The numerical simulations used the prey choice parameter as the bifurcation variable to study the possible Hopf bifurcations. The effect of alternative prey on the stability of the food chain system was derived through the theoretical and numerical results.

     

    • FullText(HTML)
  • loading
    • References(15)
  • [1]
    FREEDMAN H I,WALTMAN P.Mathematical analysis of some three-species food chain models[J].Mathematical Biosciences,1977,33(3):257-276.
    [2]
    HASTINGS A,POWELL T.Chaos in a three-species food chain[J].Ecology,1991,72(3):896-903.
    [3]
    HSU S,HWANG T,KUANG Y.A ratio-dependent food chain model and its applications to biological control[J].Mathematical Biosciences,2003,181(1):55-83.
    [4]
    GINOUX J M,ROSSETTO B,JAMET J L.Chaos in a three-dimensional Volterra-Gause model of predator-prey type[J].International Journal of Bifurcation and Chaos,2005,15(5):1689-1708.
    [5]
    PATHAK S,MAITI A,SAMANTA G P.Rich dynamics of a food chain model with Hassell-Varley type functional responses[J].Applied Mathematics and Computation,2009,208(2):303-317.
    [6]
    GEORGE A K,KOOI P I,BOER M P.Ecological consequences of global bifurcations in some food chain models[J].Mathematical Biosciences,2010,226(2):120-133.
    [7]
    STRAUSS S Y.Indirect effects in community ecology: Their definition,study and importance[J].Trends in Ecological Evolution,1991,6(7): 206-210.
    [8]
    SAHOO B,PORIA S.Diseased prey predator model with general Holling type interactions[J].Applied Mathematics and Computation,2014,226(1):83-100.
    [9]
    HUXEL G R,MCCANN K.Food web stability: The influence of trophic flows across habitats[J].American Natualist,1998,152(3):460-469.
    [10]
    HUXEL G R,MCCANN K,POLIS G A.Effects of partitioning allochthonous and autochthonous resources on food web stability[J].Ecological Research,2002,17(4):419-432.
    [11]
    SRINIVASU P D N,PRASAD B S R V,VENKATESULU M.Biological control through provision of additional food to predators: A theoretical study[J].Theoretical Population Biology,2007,72(1):111-120.
    [12]
    SAHOO B.Effects of additional foods to predators on nutrient-consumer-predator food chain model[J/OL].ISRN Biomathematics,2012.http://dx.doi.org/10.5402/2012/796783.
    [13]
    SAHOO B.Global stability of predator-prey system with alternative prey[J/OL].ISRN biotechnology,2013.http://dx.doi.org/10.5402/2013/898039.
    [14]
    SAHOO B,PORIA S.Disease control in a food chain model supplying alternative food[J].Applied Mathematical Modelling,2013,37(8):5653-5663.
    [15]
    SAHOO B,PORIA S.The chaos and control of a food chain model supplying additional food to top-predator[J].Chaos Solitons & Fractals,2014,58(1):52-64.
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Get Citation
    PDF
    XML

    Article Metrics

    Article views(734) PDF downloads(505) Cited by()
    Proportional views
    Related

    Copyright © Journal of Beijing University of Aeronautics and Astronautics

    Address: Editorial Department of Journal of Beijing University of Aeronautics and Astronautics, 37 Xueyuan Road, Haidian District, Beijing Post Code: 100191 Email: jbuaa@buaa.edu.cn

    Supported by: Beijing Renhe Information Technology Co., Ltd.    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return