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Permanence for a delayed discrete ratio-dependent predator-prey system with Holling type functional response. (English) Zbl 1063.39013

For the system \[ \begin{aligned} N_1(k+1) &= N_1(k)\exp \{b_1(k)- a_1(k)N_1(k-\tau_1)- \alpha_1(k) Z(k)N_2(k)/N_1(k)\},\\ N_2(k+1) &= N_2(k)\exp\{-b_2(k)+ \alpha_2(k)Z(k-\tau_2)\},\end{aligned} \] with the abbreviation \(Z(k)=N_1^2 (k)/(N_1^2(k)+m^2N^2_2(k))\) sufficient conditions are given such that all positive solutions are asymptotically uniformly bounded and uniformly bounded away from zero.

MSC:

39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
39A20 Multiplicative and other generalized difference equations
39A11 Stability of difference equations (MSC2000)
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