On the Solutions of Systems of Difference Equations via Tribonacci Numbers

Abstract

The main objective of this paper is to investigate the explicit form, stability character and global behavior of solutions of the following two systems of rational difference equations, n = 0, 1, ... such that their solutions are associated with Tribonacci numbers.

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

“…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. Our paper extends beyond these realms by delving into the analysis of higher-order systems and considering more diverse and complex scenarios.…”