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Stable periodic solution of the discrete periodic Leslie-Gower predator-prey model. (English) Zbl 1067.39008
For the system \(x_1(k+1)= x_1(k)\exp\{r_1- b_1x_1(k)- a_1x_2(k)\}\), \(x_2(k+ 1)= x_2(k)\exp\{r_2- a_2x_2(k)/x_1(k)\}\) a sufficient condition is given such that it is permanent. In the case of periodic coefficients sufficient conditions are given such that a periodic solution exists, and that this solution is globally stable, in case it is positive.

MSC:
39A11 Stability of difference equations (MSC2000)
92D25 Population dynamics (general)
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