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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 $$\align N_1(k+1) &= N_1(k)\exp \{b_1(k)- a_1(k)N_1(k-\tau_1)- \alpha_1(k) Z(k)N_2(k)/N_1(k)\},\\ N_2(k+1) &= N_2(k)\exp\{-b_2(k)+ \alpha_2(k)Z(k-\tau_2)\},\endalign$$ 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.

39A12Discrete version of topics in analysis
92D25Population dynamics (general)
39A20Generalized difference equations
39A11Stability of difference equations (MSC2000)
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