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Permanence and asymptotic properties of nonlinear delay difference equations. (English) Zbl 1058.39007

Summary: The asymptotic behavior of a class of nonlinear delay difference equation is studied. Some sufficient conditions are obtained for permanence and global attractivity. The results can be applied to a class of nonlinear delay difference equations and to the delay discrete logistic model. Some known results are included.

MSC:

39A11 Stability of difference equations (MSC2000)
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References:

[1] Agarwal R P.Difference Equations and Inequalities[M]. New York: Dekker, 1992. · Zbl 0925.39001
[2] Kocic V L, Ladas G.Global Behavior of Nonlinear Difference Equations of Higher Order with Applications[M]. Boston: Kluwer Academic Publishers, 1993. · Zbl 0787.39001
[3] Camouzis E, Ladas G, Rodrigues I W. On the rational recursive {\(\chi\)} n+1 = {\(\beta\)}{\(\chi\)} n 2 /(1+{\(\chi\)} n-1 2 ) [J].Computers Math Appl, 1994,28(1):37–43. · Zbl 0806.39002 · doi:10.1016/0898-1221(94)00091-3
[4] ZHANG De-cun, SHI Bao, GAI Ming-jiu. On the rational recursive sequence {\(\chi\)} n+1={\(\beta\)}{\(\chi\)} n 2 /(1+{\(\chi\)} n-1 2 ) [J].Indian J Pure Appl Math, 2001,32(5):657–663.
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