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Qualitative analysis of a fourth order difference equation
Haza Saleh Alayachi,M. S. M. Noorani,E. M. Elsayed
Keywords:Stability, periodicity, global attractor, boundedness, difference equations.
Abstract:
      In this paper, we will investigate some qualitative behavior of solutions of the following fourth order difference equation $x_{n+1}=ax_{n-1}+\frac{bx_{n-1}}{cx_{n-1}-dx_{n-3}},$ \ $n=0,1,...,$ where the initial conditions $x_{-3,}x_{-2},\ x_{-1}$\ and\ $x_{0}\ $are arbitrary real numbers and the values $a,\ b,\ c\ $and$\;d$ are\ defined as positive real numbers.