Theoretical and numerical analysis of solutions of some systems of nonlinear difference equations

Abstract

<abstract><p>In this paper, we obtain the form of the solutions of the following rational systems of difference equations</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} x_{n+1} = \dfrac{y_{n-1}z_{n}}{z_{n}\pm x_{n-2}}, \;y_{n+1} = \dfrac{z_{n-1}x_{n} }{x_{n}\pm y_{n-2}}, \ z_{n+1} = \dfrac{x_{n-1}y_{n}}{y_{n}\pm z_{n-2}}, \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>with initial values are non-zero real numbers.</p></abstract>

Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations

“…Many researchers have made significant contributions to unraveling the behavior of solved difference equations and systems, shedding light on their dynamics and stability properties. For instance, Elsayed and Alshabi [14] delved into the solution forms and stability properties of second-order systems, while Al-Basyouni and Elsayed [15] provided formulas for solutions to systems of rational difference equations of various orders, demonstrating periodicity in certain cases. Okumuş and Soykan [16] extended this exploration to two-dimensional systems associated with Tribonacci numbers.…”