Dynamical behavior and solution of nonlinear difference equation via Fibonacci sequence. (English) Zbl 1461.39001
Summary: In this paper, we study the behavior of the difference equation \(x_{n+1}=ax_n+\frac{bx_nx_{n-1}}{cx_{n-1}+dx_{n-2}}, n=0,1,\ldots,\) 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.
MSC:
| 39A10 | Additive difference equations |
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
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