Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 973869, 17 pages
http://dx.doi.org/10.1155/2012/973869
Research Article

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

1Institute of Systems Science, Northeastern University, Liaoning, Shenyang 110819, China
2Department of Mathematics, Anshan Normal University, Liaoning, Anshan 114007, China
3School 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.

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.