Dynamics of the difference equation \[ x_{n+1} = \frac {\alpha + B_1x_{n-1}+ B_3x_{n-3}+ \cdots + B_{2k+1}+ x_{n-2k-1}}{A+B_0x_n+B_2x_{n-2}+ \cdots + B_{2k}x_{n-2k}} \]. (English) Zbl 1104.39008
A class of nonlinear difference equations in rational form with nonnegative parameters and initial conditions is considered. Previous results on special cases of this class of difference equations are generalized to sufficient conditions involving the boundedness and periodic behavior of the solutions as well as the stability of the fixed points.
Reviewer: Edwin Engin Yaz (Milwaukee)
MSC:
| 39A11 | Stability of difference equations (MSC2000) |
| 39A20 | Multiplicative and other generalized difference equations |
| 39A12 | Discrete version of topics in analysis |
Keywords:
rational difference equation; global asymptotical stability; Boundedness; Periodic solution; Trichotomy character; fixed pointsReferences:
| [1] | DOI: 10.1080/1023619031000146850 · Zbl 1319.39006 · doi:10.1080/1023619031000146850 |
| [2] | DOI: 10.1201/9781420035384 · doi:10.1201/9781420035384 |
| [3] | DOI: 10.1080/1023619021000054015 · Zbl 1038.39004 · doi:10.1080/1023619021000054015 |
| [4] | DOI: 10.1016/j.amc.2004.04.002 · Zbl 1071.39009 · doi:10.1016/j.amc.2004.04.002 |
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