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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 429076, 12 pages
http://dx.doi.org/10.1155/2012/429076
Research Article

Dynamic Behaviors of a Discrete Two Species Predator-Prey System Incorporating Harvesting

Department of Mathematics, Minjiang University, Fujian, Fuzhou 350108, China

Received 2 May 2012; Revised 19 August 2012; Accepted 29 August 2012

Academic Editor: Jinde Cao

Copyright © 2012 Ting Wu. 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

A discrete two species predator-prey captured system is studied. Firstly, a sufficient condition of a positive equilibrium point for this system is obtained. Secondly, we observe that the two nonnegative equilibriums of the system are unstable through the eigenvalue discriminant method, and the positive equilibrium point is asymptotically stable by Jury criterion. Lastly, we obtain the optimal capture strategy of the system from the maximum principle by constructing a discrete Hamiltonian function. To show the feasibility of the main results, a suitable example together with its numerical simulations is illustrated in the last part of the paper. The example with certain practical significance might give an optimal scheme of the greatest economic benefits for the captors.