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The Analysis and Control for Singular Ecological‐Economic Model with Harvesting and Migration

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  • Qingling Zhang
  • Hong Niu
  • Lichun Zhao
  • Fenglan Bai

Abstract

To keep the resources renewable, a singular ecological‐economic model is proposed for the populations with harvesting and migration. The local stability and the dynamic behavior of the model are studied. Singular induced bifurcation appears when economic interest is zero, which is different from the ordinary differential models. In order to apply variable structure control to eliminate these complex behaviors, the singular model is transformed into a single‐input and single‐output model with parameter varying within definite intervals. And then, a variable structure controller is designed to make the model stable. Finally, an inshore‐offshore fishery model is given to illustrate the proposed method, and some numerical simulations are shown to demonstrate the control results.

Suggested Citation

  • Qingling Zhang & Hong Niu & Lichun Zhao & Fenglan Bai, 2012. "The Analysis and Control for Singular Ecological‐Economic Model with Harvesting and Migration," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:973869
    DOI: 10.1155/2012/973869
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    References listed on IDEAS

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    1. Zhang, Xue & Zhang, Qing-ling & Zhang, Yue, 2009. "Bifurcations of a class of singular biological economic models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1309-1318.
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    Cited by:

    1. Yi Zhang & Yueming Jie & Xinyou Meng, 2016. "The Modelling and Control of a Singular Biological Economic System in a Polluted Environment," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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