Dynamical behavior and solution of nonlinear difference equation via Fibonacci sequence |
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| Authors: | Elsayed M. Elsaye Faris Alzahrani Ibrahim Abbas N. H. Alotaibi |
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| Affiliation: | King Abdulaziz University, Faculty of Science, Mathematics Department, P. O. Box 80203, Jeddah 21589, Saudi Arabia.,King AbdulAziz University,King Abdulaziz University, Faculty of Science, Mathematics Department, P. O. Box 80203, Jeddah 21589, Saudi Arabia. and King Abdulaziz University, Faculty of Science, Mathematics Department, P. O. Box 80203, Jeddah 21589, Saudi Arabia. |
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| 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. |
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| Keywords: | Stability boundedness solution of difference equations. |
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