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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}+((bx_{n}x_{n-1})/(cx_{n-1}+dx_{n-2})),n=0,1,..., where the initial conditions x??, x??, x? 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.