On the dynamical behaviors and periodicity of difference equation of order three

Year 2022, Volume: 11 Issue: 1, 48 - 61, 30.04.2022

Ibraheem Alsulami , Elsayed Elsayed

https://doi.org/10.54187/jnrs.1037024

Abstract

The major target of our research paper is to demonstrate the boundedness, stability and periodicity of the solutions of the following third- order difference equation
$$
w_{n+1} = \alpha w_{n} +\frac {\beta+ \gamma w_{n_-2} }{\delta+\zeta w_{n-2}} , \;\;\;\; n = 0,1,2,\dots
$$
where $w_{-2}$, $w_{-1}$, and $w_{0} $ are arbitrary real numbers and the values $\alpha$, $\beta$, $\gamma$, $\delta$, and $\zeta$ are defined as positive constants.

Keywords

Periodicity, Stability, Boundedness, Difference equations

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