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 Volume 10, Number 1, 2020, Pages 282-296 Dynamical behavior and solution of nonlinear difference equation via Fibonacci sequence Elsayed M. Elsayed,Faris Alzahrani,Ibrahim Abbas,N. H. Alotaibi Keywords:Stability, boundedness, solution of difference equations. Abstract: In this paper, we study the behavior of the difference equation $x_{n+1}=ax_{n}+\dfrac{bx_{n}x_{n-1}}{cx_{n-1}+dx_{n-2}},~n=0,1,\ldots,$ where the initial conditions $x_{-2},\ x_{-1},\ x_{0}$ are arbitrary positive real numbers and $a,b,c,d$ are positive constants. Also, we give the solution of some special cases of this equation. PDF      Download reader