Global behavior of the difference equation x n + 1 = a x n - 3 b + c x n - 1 x n - 3

Raafat Abo-Zeid

Archivum Mathematicum (2015)

  • Volume: 051, Issue: 2, page 77-85
  • ISSN: 0044-8753

Abstract

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In this paper, we introduce an explicit formula and discuss the global behavior of solutions of the difference equation x n + 1 = a x n - 3 b + c x n - 1 x n - 3 , n = 0 , 1 , ⋯ where a , b , c are positive real numbers and the initial conditions x - 3 , x - 2 , x - 1 , x 0 are real numbers.

How to cite

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Abo-Zeid, Raafat. "Global behavior of the difference equation $x_{n+1}=\frac{ax_{n-3} }{b+ cx_{n-1}x_{n-3}}$." Archivum Mathematicum 051.2 (2015): 77-85. <http://eudml.org/doc/270130>.

@article{Abo2015,
abstract = {In this paper, we introduce an explicit formula and discuss the global behavior of solutions of the difference equation \[ x\_\{n+1\}=\frac\{ax\_\{n-3\} \}\{b+ cx\_\{n-1\}x\_\{n-3\}\}\,,\qquad n=0,1,\dots \] where $a,b,c$ are positive real numbers and the initial conditions $x_\{-3\}$, $x_\{-2\}$, $x_\{-1\}$, $x_0$ are real numbers.},
author = {Abo-Zeid, Raafat},
journal = {Archivum Mathematicum},
keywords = {difference equation; periodic solution; convergence},
language = {eng},
number = {2},
pages = {77-85},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Global behavior of the difference equation $x_\{n+1\}=\frac\{ax_\{n-3\} \}\{b+ cx_\{n-1\}x_\{n-3\}\}$},
url = {http://eudml.org/doc/270130},
volume = {051},
year = {2015},
}

TY - JOUR
AU - Abo-Zeid, Raafat
TI - Global behavior of the difference equation $x_{n+1}=\frac{ax_{n-3} }{b+ cx_{n-1}x_{n-3}}$
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 2
SP - 77
EP - 85
AB - In this paper, we introduce an explicit formula and discuss the global behavior of solutions of the difference equation \[ x_{n+1}=\frac{ax_{n-3} }{b+ cx_{n-1}x_{n-3}}\,,\qquad n=0,1,\dots \] where $a,b,c$ are positive real numbers and the initial conditions $x_{-3}$, $x_{-2}$, $x_{-1}$, $x_0$ are real numbers.
LA - eng
KW - difference equation; periodic solution; convergence
UR - http://eudml.org/doc/270130
ER -

References

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