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.
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