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    Finite Time Blowup in a Realistic Food-Chain Model

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    Type
    Article
    Authors
    Parshad, Rana cc
    Ait Abderrahmane, Hamid
    Upadhyay, Ranjit Kumar
    Kumari, Nitu cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2013-06-13
    Online Publication Date
    2013-06-13
    Print Publication Date
    2013
    Permanent link to this record
    http://hdl.handle.net/10754/550710
    
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    Abstract
    We investigate a realistic three-species food-chain model, with generalist top predator. The model based on a modified version of the Leslie-Gower scheme incorporates mutual interference in all the three populations and generalizes several other known models in the ecological literature. We show that the model exhibits finite time blowup in certain parameter range and for large enough initial data. This result implies that finite time blowup is possible in a large class of such three-species food-chain models. We propose a modification to the model and prove that the modified model has globally existing classical solutions, as well as a global attractor. We reconstruct the attractor using nonlinear time series analysis and show that it pssesses rich dynamics, including chaos in certain parameter regime, whilst avoiding blowup in any parameter regime. We also provide estimates on its fractal dimension as well as provide numerical simulations to visualise the spatiotemporal chaos.
    Citation
    Finite Time Blowup in a Realistic Food-Chain Model 2013, 2013:1 ISRN Biomathematics
    Publisher
    Hindawi Limited
    Journal
    ISRN Biomathematics
    DOI
    10.1155/2013/424062
    Additional Links
    http://www.hindawi.com/journals/isrn.biomathematics/2013/424062/
    ae974a485f413a2113503eed53cd6c53
    10.1155/2013/424062
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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