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On a Leslie-Gower predator-prey model incorporating a prey refuge. (English) Zbl 1167.92032
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.

##### MSC:
 92D40 Ecology 34D20 Stability of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations
##### Keywords:
Leslie-Gower model; Lyapunov function
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##### References:
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