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Journal of Applied MathematicsVolume 2012 2012, Article ID 973869, 17 pages

Research Article

Institute of Systems Science, Northeastern University, Liaoning, Shenyang 110819, China

Department of Mathematics, Anshan Normal University, Liaoning, Anshan 114007, China

School of Science, Dalian Jiaotong University, Liaoning, Dalian 116028, China

Received 12 March 2012; Accepted 11 April 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 Qingling Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.

Autor: Qingling Zhang, Hong Niu, Lichun Zhao, and Fenglan Bai



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