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Zbl 1213.37129
Zhang, Na; Chen, Fengde; Su, Qianqian; Wu, Ting
Dynamic behaviors of a harvesting Leslie-Gower predator-prey model. (English)
[J] Discrete Dyn. Nat. Soc. 2011, Article ID 473949, 14 p. (2011). ISSN 1026-0226; ISSN 1607-887X/e

Summary: 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.

MSC 2000:: *37N25 Dynamical systems in biology
92D25 Population dynamics

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