Dynamics and Expression of Solution of a Sixth Order Difference Equation

Authors : Abdul KHALİQ

Pages : 89-102

Doi:10.33187/jmsm.929981

View : 16 | Download : 8

Publication Date : 2021-08-31

Article Type : Research Paper

Abstract :This paper deals with the solution behavior and periodic nature of the solutions of the difference equation $$ s_{n+1}=\alpha s_{n}+\dfrac{\beta s_{n}s_{n-4}}{\gamma s_{n-4}+\delta s_{n-5} },\;\;\;n=0,1,... $$ {\Large \noindent }where the initial conditions $s_{-5},\ s_{-4},\ s_{-3},\ s_{-2},\ s_{-1},\ s_{0}$ are arbitrary positive real numbers and $\alpha ,\ \beta ,\ \gamma ,\ \delta \ $are positive constants. Also we obtain the closed form of the solutions of some special cases of this equation.
Keywords : stability, form of solution, periodicity, rational difference equation