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.


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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