Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 473949, 14 pages
doi:10.1155/2011/473949
Research Article

Dynamic Behaviors of a Harvesting Leslie-Gower Predator-Prey Model

1College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, Fujian, China
2Department of Mathematics and Physics, Minjiang College, Fuzhou 350108, Fujian, China

Received 24 October 2010; Accepted 8 February 2011

Academic Editor: Prasanta K. Panigrahi

Copyright © 2011 Na 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

A Leslie-Gower predator-prey model incorporating harvesting is studied. By constructing a suitable Lyapunov function, we show that the unique positive equilibrium of the system is globally stable, which means that suitable harvesting has no influence on the persistent property of the harvesting system. After that, detailed analysis about the influence of harvesting is carried out, and an interesting finding is that under some suitable restriction, harvesting has no influence on the final density of the prey species, while the density of predator species is strictly decreasing function of the harvesting efforts. For the practical significance, the economic profit is considered, sufficient conditions for the presence of bionomic equilibrium are given, and the optimal harvesting policy is obtained by using the Pontryagin's maximal principle. At last, an example is given to show that the optimal harvesting policy is realizable.