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THE DYNAMICAL BEHAVIOR OF A HIGHER ORDER DIFFERENCE EQUATION
Keywords:
difference equation, equilibrium point, solution, global behavior.DOI:
https://doi.org/10.17654/0974165822048Abstract
This paper shows the global behavior of the nonnegative equilibrium points of the difference equation
$$
x_{n+1}=\frac{\alpha x_{n-(2 k+3)}}{\beta+\gamma x_{n-(k+1)}^r x_{n-(2 k+3)}^s}, \quad n=0,1, \ldots,
$$
where $\alpha, \beta, \gamma$ are positive parameters, initial conditions are nonnegative real numbers, $r, s \geq 1$ and $k$ is a natural number.
Received: September 14, 2022
Accepted: October 28, 2022
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