Global Dynamics of Certain Non-symmetric Second Order Difference Equation With Quadratic Term
DOI:
https://doi.org/10.5644/SJM.15.02.02Keywords:
Difference equation, equilibrium, period-two solutions, local stability, global stabilityAbstract
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.
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