Global Dynamics of Certain Non-symmetric Second Order Difference Equation With Quadratic Term

We investigate global dynamics of the equation\begin{equation*}x_{n+1}=\frac{x_{n-1}+F}{ax_{n}^2+f},\text{ \ }n=0,1,2,...,\end{equation*}where the parameters $a,F$ and $f$ are positive numbers and the initial conditions $x_{-1},x_{0}$ are arbitrary nonnegative numbers such that $x_{-1}+x_{0}>0$....

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Bibliographic Details
Published in:Sarajevo journal of mathematics 2020-02, Vol.15 (2), p.155-167
Main Authors: Garić-Demirović, M., Hrustić, S., Moranjkić, S.
Format: Article
Language:English
Online Access:Get full text
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Summary:We investigate global dynamics of the equation\begin{equation*}x_{n+1}=\frac{x_{n-1}+F}{ax_{n}^2+f},\text{ \ }n=0,1,2,...,\end{equation*}where the parameters $a,F$ and $f$ are positive numbers and the initial conditions $x_{-1},x_{0}$ are arbitrary nonnegative numbers such that $x_{-1}+x_{0}>0$. The existence and local stability of the unique positive equilibrium are analyzed algebraically. We characterize the global dynamics of this equation with the basins of attraction of its equilibrium point and periodic solutions.
ISSN:1840-0655
2233-1964
DOI:10.5644/SJM.15.02.02