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Zbl 1063.39013
Fan, Yong-Hong; Li, Wan-Tong
Permanence for a delayed discrete ratio-dependent predator-prey system with Holling type functional response. (English)
[J] J. Math. Anal. Appl. 299, No. 2, 357-374 (2004). ISSN 0022-247X

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.
[Lothar Berg (Rostock)]

MSC 2000:: *39A12 Discrete version of topics in analysis
92D25 Population dynamics
39A20 Generalized difference equations
39A11 Stability of difference equations

Keywords: system of difference equations; discrete predator-prey model; permanence; asymptotically bounded solution; positive solutions; functional response

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