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Persistence and global attractivity in the model \(A_{n+1}=qA_n+F_n(A_n,A_{n-1},\dots,A_{n-m})\). (English) Zbl 1221.39022

Summary: First, we prove the uniform persistence for discrete model \[ A_{n+1}=qA_{n}+F_{n}(A_{n},A_{n-1},\dots,A_{n-m}) \] of population growth, when \(F_n:(0,\infty)^{m+1}\to(0,\infty)\) is continuous in all variables. Second, we investigation the effect of delay \(m\) on the global attractivity of the unique positive equilibrium.

MSC:

39A30 Stability theory for difference equations
92D25 Population dynamics (general)
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References:

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