[02027] Understanding Difference Equation System Models using Telescoping Sums Method

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G710

Type : Contributed Talk

Abstract : Difference equations frequently appear as discrete mathematical models of various biological and environmental phenomena. In this paper, the authors study the following systems:
\begin{equation*}
x_{n+1} = \dfrac{x_{n-3}}{\pm 1 \pm y_n x_{n-1} y_{n-2} x_{n-3}},\ \
y_{n+1} = \dfrac{y_{n-3}}{\pm 1 \pm x_n y_{n-1} x_{n-2} y_{n-3}},
\end{equation*}
which were first considered by Elsayed in 2015, and results were proven using mathematical induction.
This time, the authors present the solution forms of each system using telescoping sums technique. The advantages and disadvantages of the two methods are discussed. Boundedness and convergence of solutions shall be presented.