On the dynamical behaviors and periodicity of difference equation of order three - Elsayed Elsayed; Ibraheem Alsulami (Journal of New Results in Science)
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 $$ w_{n+1} = α w_{n} +\frac {β+ γ w_{n_-2} }{δ+ζ w_{n-2}} , \;\;\;\; n = 0,1,2,…$$ where $w_{-2}$, $w_{-1}$, and $w_{0} $ are arbitrary real numbers and the values $α$, $β$, $γ$, $δ$, and $ζ$ are defined as positive constants.