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On a system of rational difference equations. (English) Zbl 1078.39006

The authors study several qualitative properties of the system \[ x_{n+1}=(h+x_n)(a+y_n)^{-1}\;,\;y_{n+1}=y_n(b+x_n)^{-1}\;,\;n\geq 0 \] with \(a>0\), \(b>0\), \(h>0\), \(x_0\geq 0\), \(y_0\geq 0\). There are tackled stability by the first approximation, monotone maps and global behavior, global attractiveness results and rates of convergence. Connections to already known results are presented.

MSC:

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
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References:

[1] Alligood KT, CHAOS An Introduction to Dynamical Systems (1997)
[2] DOI: 10.1016/S0898-1221(01)00326-1 · Zbl 1001.39017 · doi:10.1016/S0898-1221(01)00326-1
[3] DOI: 10.1016/S0362-546X(02)00294-8 · Zbl 1019.39006 · doi:10.1016/S0362-546X(02)00294-8
[4] Dancer EN, Journal für die Reine und Angewandte Mathematik 419 pp 125– (1991)
[5] Elaydi S, An Introduction to Difference Equations (1999) · doi:10.1007/978-1-4757-3110-1
[6] Elaydi S, Discrete Chaos (2000)
[7] DOI: 10.1007/BF00160333 · Zbl 0735.92023 · doi:10.1007/BF00160333
[8] DOI: 10.1016/0022-247X(92)90167-C · Zbl 0778.93012 · doi:10.1016/0022-247X(92)90167-C
[9] DOI: 10.1016/0040-5809(76)90045-9 · Zbl 0338.92020 · doi:10.1016/0040-5809(76)90045-9
[10] Hess P, Periodic-parabolic Boundary Value Problems and Positivity 247 (1991) · Zbl 0731.35050
[11] DOI: 10.1016/0362-546X(91)90097-K · Zbl 0743.35033 · doi:10.1016/0362-546X(91)90097-K
[12] Kocic VL, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (1993) · doi:10.1007/978-94-017-1703-8
[13] DOI: 10.1201/9781420035384 · doi:10.1201/9781420035384
[14] DOI: 10.1201/9781420035353 · doi:10.1201/9781420035353
[15] Kulenović MRS, Radovi Matematicki 11 pp 59– (2002)
[16] DOI: 10.1080/10236190211954 · Zbl 1002.39014 · doi:10.1080/10236190211954
[17] Robinson C, Stability, Symbolic Dynamics, and Chaos (1995)
[18] Selgrade JF, Journal of Mathematical Biology 25 pp 477– (1987) · Zbl 0634.92008 · doi:10.1007/BF00276194
[19] DOI: 10.1080/10236199708808108 · Zbl 0907.39004 · doi:10.1080/10236199708808108
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