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

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Journal of New Results in Science
Volume:11 Issue:1
On the dynamical behaviors and periodicity of difference equation of order three

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

Authors : Ibraheem ALSULAMİ, Elsayed ELSAYED

Pages : 48-61

Doi:10.54187/jnrs.1037024

View : 46 | Download : 11

Publication Date : 2022-04-30

Article Type : Research Paper

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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