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Zbl 1167.92032
Chen, Fengde; Chen, Liujuan; Xie, Xiangdong
On a Leslie-Gower predator-prey model incorporating a prey refuge. (English)
[J] Nonlinear Anal., Real World Appl. 10, No. 5, 2905-2908 (2009). ISSN 1468-1218

The authors propose a Leslie-Gower predator-prey model incorporating a prey refuge, which is an extension of the model first introduced by Leslie where the carrying capacity of the predator's environment is proportional to the number of prey. By constructing a Korobeinikov-type Lyapunov function, it is shown that for this ecosystem prey refuge has no influence on the persistence property of the system as the unique positive equilibrium of the system is globally stable. Also, increasing the amount of refuge can increase prey density. As far as the predator species is concerned, under certain conditions, increasing the amount of prey refuge can decrease the predator density. There exists a threshold such that for the prey refuge smaller than this threshold, increasing the amount of prey refuge can increase the predator density, and if the prey refuge is larger than the threshold, increasing the amount of prey refuge can decrease the predator density.
[J. M. Tchuenche (Dar es Salaam)]

MSC 2000:: *92D40 Ecology
34D20 Lyapunov stability of ODE
34D23 Global stability

Keywords: Leslie-Gower model; Lyapunov function

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