@article{article_1037024, title={On the dynamical behaviors and periodicity of difference equation of order three}, journal={Journal of New Results in Science}, volume={11}, pages={48–61}, year={2022}, DOI={10.54187/jnrs.1037024}, author={Alsulami, Ibraheem and Elsayed, Elsayed}, keywords={Periodicity, Stability, Boundedness, Difference equations}, 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.}, number={1}, publisher={Tokat Gaziosmanpasa University}